In this paper, we introduce two new iterative algorithms for finding a common element of the set of solutions of a general equilibrium problem and the set of solutions of the variational inequality for an inverse-stro...In this paper, we introduce two new iterative algorithms for finding a common element of the set of solutions of a general equilibrium problem and the set of solutions of the variational inequality for an inverse-strongly monotone operator and the set of common fixed points of two infinite families of relatively nonexpansive mappings or the set of common fixed points of an infinite family of relatively quasi-nonexpansive mappings in Banach spaces. Then we study the weak convergence of the two iterative sequences. Our results improve and extend the results announced by many others.展开更多
In this paper,we develop the criterion on the upper semi-continuity of random attractors by a weak-to-weak limit replacing the usual norm-to-norm limit.As an application,we obtain the convergence of random attractors ...In this paper,we develop the criterion on the upper semi-continuity of random attractors by a weak-to-weak limit replacing the usual norm-to-norm limit.As an application,we obtain the convergence of random attractors for non-autonomous stochastic reactiondiffusion equations on unbounded domains,when the density of stochastic noises approaches zero.The weak convergence of solutions is proved by means of Alaoglu weak compactness theorem.A differentiability condition on nonlinearity is omitted,which implies that the existence conditions for random attractors are sufficient to ensure their upper semi-continuity.These results greatly strengthen the upper semi-continuity notion that has been developed in the literature.展开更多
The purpose of this paper is to prove a new weak convergence theorem for a finite family of asymptotically nonexpansive mappings in uniformly convex Banach space.
In this paper, we prove that two-parameter Volterra multifractional process can be approximated in law in the topology of the anisotropic Besov spaces by the family of processes {Bn（s, t）}n∈N defined by Bn（s,t）=...In this paper, we prove that two-parameter Volterra multifractional process can be approximated in law in the topology of the anisotropic Besov spaces by the family of processes {Bn（s, t）}n∈N defined by Bn（s,t）=∫0^s∫0^tKa（s）（s,u）Kβ（t）（t,v）θn（u,u）dudu,where {θn（u, v））,n∈N is a family of processes, converging in law to a Brownian sheet as n -＊ oo, based on the well known Donsker＇s theorem.展开更多
A special approximation to Rosenblatt process with the finite-time interval representation was obtained. The construction of approximation family was based on the Poisson process. The proof to the approximation was di...A special approximation to Rosenblatt process with the finite-time interval representation was obtained. The construction of approximation family was based on the Poisson process. The proof to the approximation was divided into two aspects. Firstly, the approximation family was tight using the methods given by Billingsley; secondly, the finite-dimension distributions of approximation family converged weakly to the Rosenblatt process by proving the convergence of the corresponding characteristic functions.展开更多
This paper investigates the ergodicity and weak convergence of transition probabilities for two-dimensional stochastic primitive equations driven by multiplicative noise.The existence of invariant measures is establis...This paper investigates the ergodicity and weak convergence of transition probabilities for two-dimensional stochastic primitive equations driven by multiplicative noise.The existence of invariant measures is established using the classical Krylov-Bogoliubov theory.The uniqueness of invariant measures and the weak convergence of transition probabilities are demonstrated through the application of the asymptotic coupling method and Foias-Prodi estimate.展开更多
In this paper, we establish a Rosenthal-type inequality of the maximum of partial sums for ρ^- -mixing random fields. As its applications we get the Hájeck -Rènyi inequality and weak convergence of sums of ...In this paper, we establish a Rosenthal-type inequality of the maximum of partial sums for ρ^- -mixing random fields. As its applications we get the Hájeck -Rènyi inequality and weak convergence of sums of ρ^- -mixing sequence. These results extend related results for NA sequence and p^＊ -mixing random fields,展开更多
We study the problem of the approximation in law of the Rosenblatt sheet. We prove the convergence in law of two families of process to the Rosenblatt sheet： the first one is constructed from a Poisson process in the...We study the problem of the approximation in law of the Rosenblatt sheet. We prove the convergence in law of two families of process to the Rosenblatt sheet： the first one is constructed from a Poisson process in the plane and the second one is based on random walks.展开更多
In this paper, by using Mann＇s iteration process we will establish several weak convergence theorems for approximating a fixed point of k-strictly pseudocontractive mappings with respect to p in p-uniformly convex Ba...In this paper, by using Mann＇s iteration process we will establish several weak convergence theorems for approximating a fixed point of k-strictly pseudocontractive mappings with respect to p in p-uniformly convex Banach spaces. Our results answer partially the open question proposed by Marino and Xu, and extend Reich＇s theorem from nonexpansive mappings to k-strict pseudocontractive mappings.展开更多
Let G be a semitopological semigroup. Let C be a closed convex subset of a uniformly convex Banaeh space E with a Frechet differentiable norm, and T = {Tt ： t ∈ G} be a continuous representation of G as nearly asymp...Let G be a semitopological semigroup. Let C be a closed convex subset of a uniformly convex Banaeh space E with a Frechet differentiable norm, and T = {Tt ： t ∈ G} be a continuous representation of G as nearly asymptotically nonexpansive type mappings of C into itself such that the common fixed point set F（T） of T in C is nonempty. It is shown that if G is right reversible, then for each almost-orbit u（.） of T, ∩s∈G ^-CO{u（t） ： t ≥ s} ∩ F（T） consists of at most one point. Furthermore, ∩s∈G ^-CO{Ttx ： t ≥ s} ∩ F（T） is nonempty for each x ∈ C if and only if there exists a nonlinear ergodic retraction P of C onto F（T） such that PTs - TsP = P for all s ∈ G and Px ∈^-CO{Ttx ： s ∈ G} for each x ∈ C. This result is applied to study the problem of weak convergence of the net {u（t） ： t ∈ G} to a common fixed point of T.展开更多
In this paper, it is shown that there is a gap in the paper [Chidume, C. E., Shahzad, N.： Weak convergence theorems for a finite family of strict pseudo-contractions. Nonlinear Anal., 72, 1257–1265（2010）], consequ...In this paper, it is shown that there is a gap in the paper [Chidume, C. E., Shahzad, N.： Weak convergence theorems for a finite family of strict pseudo-contractions. Nonlinear Anal., 72, 1257–1265（2010）], consequently, the main results of the paper do not hold in uniformly smooth Banach spaces. Meanwhile, it is also shown that the main results（Lemma 3.4, Theorems 3.5–3.6, 3.8–3.9） in the paper [Cholamjiak, P., Suantai, S.： Weak convergence theorems for a countable family of strict pseudo-contractions in Banach spaces. Fixed Point Theory Appl., 2010, Article ID 632137, 16 pages（2010）] do not hold in Lpfor p 〉 3. Finally, some modified results are presented in the setting of uniformly smooth and uniformly convex Banach spaces which include Lpfor p ≥ 2 as special cases. Furthermore, our arguments are also different from the ones given by the authors above.展开更多
Let{ξt,t∈Zd}be a nonuniform 4-mixing strictly stationary real random field with Efo=0,E|f0²+6<∞for some 0<8<1.A sufficient condition is given for the sequence of partial sum set-indexed process{Zn(A),...Let{ξt,t∈Zd}be a nonuniform 4-mixing strictly stationary real random field with Efo=0,E|f0²+6<∞for some 0<8<1.A sufficient condition is given for the sequence of partial sum set-indexed process{Zn(A),A E A}to converge to Brownian motion.By a direct calculation,the author ahows that the result holds for a more general class of set index A,where A is assurned only to have the metric entropy exponentr,0<r<1.and the rate of nonuniform p-mixing is weakened.The result obtained essentially improve those given by Chen[1)and Goldie,Greenwood[6],etc.展开更多
Skorokhod's representation theorem states that if on a Polish space,there is a weakly convergent sequence of probability measures μnw→μ0,as n →∞,then there exist a probability space(Ω,F,P) and a sequence of ...Skorokhod's representation theorem states that if on a Polish space,there is a weakly convergent sequence of probability measures μnw→μ0,as n →∞,then there exist a probability space(Ω,F,P) and a sequence of random elements Xnsuch that Xn→ X almost surely and Xnhas the distribution function μn,n = 0,1,2,... We shall extend the Skorokhod representation theorem to the case where if there are a sequence of separable metric spaces Sn,a sequence of probability measures μnand a sequence of measurable mappings n such that μnn-1w→μ0,then there exist a probability space(Ω,F,P) and Sn-valued random elements Xndefined on Ω,with distribution μnand such that n(Xn) → X0 almost surely. In addition,we present several applications of our result including some results in random matrix theory,while the original Skorokhod representation theorem is not applicable.展开更多
Weak convergence of Markov processes is studied by means of Dirichlet forms and two theorems for weak convergence of Hunt processes on general metric spaces are established.As applications,examples for weak convergenc...Weak convergence of Markov processes is studied by means of Dirichlet forms and two theorems for weak convergence of Hunt processes on general metric spaces are established.As applications,examples for weak convergence of symmetric or non symmetric Dirichlet processes on finite and infinite spaces are given.展开更多
In this paper,we introduce a new iterative scheme for finding the common element of the set of solutions of an equilibrium problem,the set of solutions of variational inequalities for an α-inversely strongly monotone...In this paper,we introduce a new iterative scheme for finding the common element of the set of solutions of an equilibrium problem,the set of solutions of variational inequalities for an α-inversely strongly monotone operator and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and 2-uniformly convex Banach space.Some weak convergence theorems are obtained,to extend the previous work.展开更多
This paper considers diffusion processes {X^(?)(t)} on R^2, which are perturbations of dynamical system {X(t)} (dX(t)=b(X(t))dt) on R^2. By means of weak convergence of probability measures, the authors characterize t...This paper considers diffusion processes {X^(?)(t)} on R^2, which are perturbations of dynamical system {X(t)} (dX(t)=b(X(t))dt) on R^2. By means of weak convergence of probability measures, the authors characterize the limit behavior for empirical measures of {X^(?)(t)} in a neighborhood domain of saddle point of the dynamical system as the perturbations tend to zero.展开更多
The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generali...The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generalized functions and the convergence is weak convergence in the sense of the convergence of continuous linear functionals defining them. The figures show that the approximations of the Fourier series possess oscillations around the function which they represent in a broad band embedding them. This is some analogue to the Gibbs phenomenon. A modification of Fourier series by expansion in powers cosn(x)for the symmetric part of functions and sin(x)cosn−1(x)for the antisymmetric part (analogous to Taylor series) is discussed and illustrated by examples. The Fourier series and their convergence behavior are illustrated also for some 2π-periodic delta-function-like sequences connected with the Poisson theorem showing non-vanishing oscillations around the singularities similar to the Gibbs phenomenon in the neighborhood of discontinuities of functions. .展开更多
The almost convergent function which was introduced by Raimi [6] and discussed by Ho [4], Das and Nanda [2, 3], is the continuous analogue of almost convergent sequences （see [5]）. In this paper, we establish the Ta...The almost convergent function which was introduced by Raimi [6] and discussed by Ho [4], Das and Nanda [2, 3], is the continuous analogue of almost convergent sequences （see [5]）. In this paper, we establish the Tauberian conditions and the Cauchy criteria for weak almost convergent functions on R2＋ .展开更多
In this paper we study the Freidlin-Wentzell's large deviation principle for the following nonlinear fractional stochastic heat equation driven by Gaussian noise∂/∂tu^(ε)=D_(δ)^(α)(t,x)+√εσ(u^(ε)(t,x))W(t,x...In this paper we study the Freidlin-Wentzell's large deviation principle for the following nonlinear fractional stochastic heat equation driven by Gaussian noise∂/∂tu^(ε)=D_(δ)^(α)(t,x)+√εσ(u^(ε)(t,x))W(t,x),(t,x)∈[0,T]×R,where D_(δ)^(α)is a nonlocal fractional differential operator and W is the Gaussian noise which is white in time and behaves as a fractional Brownian motion with Hurst index H satisfying 3-α/4<H<1/2,in the space variable.The weak convergence approach plays an important role.展开更多
Several results on iterative methods for equilibrium problems have been proposed and studied in the literature.Most of these results are obtained when the associated bifunction of the equilibrium problem is either a m...Several results on iterative methods for equilibrium problems have been proposed and studied in the literature.Most of these results are obtained when the associated bifunction of the equilibrium problem is either a monotone or pseudomonotone operator.Results on iterative methods for equilibrium problems without monotonicity conditions on the bifunction are still few in the literature.In this paper,we study equilibrium problems for which the underlined bifunction is not assumed any form of monotonicity.We propose two weakly convergent iterative algorithms and one strongly convergent algorithm.We obtain our convergence results without assuming either monotonicity or pseudomonotonicity condition on the bifunction.Our proposed algorithms are tested numerically to be more efficient and faster than some few available algorithms for equilibrium problems without monotonicity in the literature.展开更多
文摘In this paper, we introduce two new iterative algorithms for finding a common element of the set of solutions of a general equilibrium problem and the set of solutions of the variational inequality for an inverse-strongly monotone operator and the set of common fixed points of two infinite families of relatively nonexpansive mappings or the set of common fixed points of an infinite family of relatively quasi-nonexpansive mappings in Banach spaces. Then we study the weak convergence of the two iterative sequences. Our results improve and extend the results announced by many others.
文摘In this paper,we develop the criterion on the upper semi-continuity of random attractors by a weak-to-weak limit replacing the usual norm-to-norm limit.As an application,we obtain the convergence of random attractors for non-autonomous stochastic reactiondiffusion equations on unbounded domains,when the density of stochastic noises approaches zero.The weak convergence of solutions is proved by means of Alaoglu weak compactness theorem.A differentiability condition on nonlinearity is omitted,which implies that the existence conditions for random attractors are sufficient to ensure their upper semi-continuity.These results greatly strengthen the upper semi-continuity notion that has been developed in the literature.
文摘The purpose of this paper is to prove a new weak convergence theorem for a finite family of asymptotically nonexpansive mappings in uniformly convex Banach space.
基金partially supported by National Natural Science Foundation of China(Grant Nos.1140131311771209)+6 种基金partially supported by National Natural Science Foundation of China(Grant No.11426036)Natural Science Foundation of Jiangsu Province(Grant No.BK20161579)China Postdoctoral Science Foundation(Grant Nos.2014M5603682015T80475)2014 Qing Lan ProjectNatural Science Foundation of Anhui Province(Grant No.1408085QA10)Key Natural Science Foundation of Anhui Education Commission(Grant No.KJ2016A453)
文摘In this paper, we prove that two-parameter Volterra multifractional process can be approximated in law in the topology of the anisotropic Besov spaces by the family of processes {Bn（s, t）}n∈N defined by Bn（s,t）=∫0^s∫0^tKa（s）（s,u）Kβ（t）（t,v）θn（u,u）dudu,where {θn（u, v））,n∈N is a family of processes, converging in law to a Brownian sheet as n -＊ oo, based on the well known Donsker＇s theorem.
基金National Natural Science Foundation of China(No. 11171062)Innovation Program of Shanghai Municipal Education Commission,China(No. 12ZZ063)Natural Science Foundation of Bengbu College,China(No. 2010ZR10)
文摘A special approximation to Rosenblatt process with the finite-time interval representation was obtained. The construction of approximation family was based on the Poisson process. The proof to the approximation was divided into two aspects. Firstly, the approximation family was tight using the methods given by Billingsley; secondly, the finite-dimension distributions of approximation family converged weakly to the Rosenblatt process by proving the convergence of the corresponding characteristic functions.
基金supported in part by the NSFC(12171084,12326367)the Jiangsu Provincial Scientific Research Center of Applied Mathematics(BK20233002)the fundamental Research Funds for the Central Universities(RF1028623037)。
文摘This paper investigates the ergodicity and weak convergence of transition probabilities for two-dimensional stochastic primitive equations driven by multiplicative noise.The existence of invariant measures is established using the classical Krylov-Bogoliubov theory.The uniqueness of invariant measures and the weak convergence of transition probabilities are demonstrated through the application of the asymptotic coupling method and Foias-Prodi estimate.
基金Supported by Scientific research project of education department of Zhejiang Province(No.20051897)
文摘In this paper, we establish a Rosenthal-type inequality of the maximum of partial sums for ρ^- -mixing random fields. As its applications we get the Hájeck -Rènyi inequality and weak convergence of sums of ρ^- -mixing sequence. These results extend related results for NA sequence and p^＊ -mixing random fields,
基金The authors would like to thank the anonymous referees whose remarks and suggestions greatly improved the presentation of the paper. The authors would also like to thank Professor Yimin Xiao, Michigan State University, USA, for stimulating discussion. Guangjun Shen was supported in part by the National Natural Science Foundation of China （Grant No. 11271020） Dongjin Zhu was supported in part by the Key Natural Science Foundation of the Anhui Educational Committee （KJ2012ZD01） and the Philosophy and Social Science Planning Foundation of Anhui Province （AHSKll-12D~28）.
文摘We study the problem of the approximation in law of the Rosenblatt sheet. We prove the convergence in law of two families of process to the Rosenblatt sheet： the first one is constructed from a Poisson process in the plane and the second one is based on random walks.
基金Supported by National Science Foundation of China(60872095)Natural Science Foundation of Zhejiang Province(Y606093)K.C.Wong Magna Fund in Ningbo University and Ningbo Natural Science Foundation(2008A610018).
文摘In this paper, by using Mann＇s iteration process we will establish several weak convergence theorems for approximating a fixed point of k-strictly pseudocontractive mappings with respect to p in p-uniformly convex Banach spaces. Our results answer partially the open question proposed by Marino and Xu, and extend Reich＇s theorem from nonexpansive mappings to k-strict pseudocontractive mappings.
基金supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE, Chinathe Dawn Program Foundation in Shanghai
文摘Let G be a semitopological semigroup. Let C be a closed convex subset of a uniformly convex Banaeh space E with a Frechet differentiable norm, and T = {Tt ： t ∈ G} be a continuous representation of G as nearly asymptotically nonexpansive type mappings of C into itself such that the common fixed point set F（T） of T in C is nonempty. It is shown that if G is right reversible, then for each almost-orbit u（.） of T, ∩s∈G ^-CO{u（t） ： t ≥ s} ∩ F（T） consists of at most one point. Furthermore, ∩s∈G ^-CO{Ttx ： t ≥ s} ∩ F（T） is nonempty for each x ∈ C if and only if there exists a nonlinear ergodic retraction P of C onto F（T） such that PTs - TsP = P for all s ∈ G and Px ∈^-CO{Ttx ： s ∈ G} for each x ∈ C. This result is applied to study the problem of weak convergence of the net {u（t） ： t ∈ G} to a common fixed point of T.
基金Supported by National Natural Science Foundation of China(Grant Nos.10771050,11071053)
文摘In this paper, it is shown that there is a gap in the paper [Chidume, C. E., Shahzad, N.： Weak convergence theorems for a finite family of strict pseudo-contractions. Nonlinear Anal., 72, 1257–1265（2010）], consequently, the main results of the paper do not hold in uniformly smooth Banach spaces. Meanwhile, it is also shown that the main results（Lemma 3.4, Theorems 3.5–3.6, 3.8–3.9） in the paper [Cholamjiak, P., Suantai, S.： Weak convergence theorems for a countable family of strict pseudo-contractions in Banach spaces. Fixed Point Theory Appl., 2010, Article ID 632137, 16 pages（2010）] do not hold in Lpfor p 〉 3. Finally, some modified results are presented in the setting of uniformly smooth and uniformly convex Banach spaces which include Lpfor p ≥ 2 as special cases. Furthermore, our arguments are also different from the ones given by the authors above.
文摘Let{ξt,t∈Zd}be a nonuniform 4-mixing strictly stationary real random field with Efo=0,E|f0²+6<∞for some 0<8<1.A sufficient condition is given for the sequence of partial sum set-indexed process{Zn(A),A E A}to converge to Brownian motion.By a direct calculation,the author ahows that the result holds for a more general class of set index A,where A is assurned only to have the metric entropy exponentr,0<r<1.and the rate of nonuniform p-mixing is weakened.The result obtained essentially improve those given by Chen[1)and Goldie,Greenwood[6],etc.
基金supported by the Fundamental Research Funds for the Central UniversitiesProgram for Changjiang Scholars and Innovative Research Team in UniversityNational Natural Science Foundation of China(Grant Nos.11301063 and 11171057)
文摘Skorokhod's representation theorem states that if on a Polish space,there is a weakly convergent sequence of probability measures μnw→μ0,as n →∞,then there exist a probability space(Ω,F,P) and a sequence of random elements Xnsuch that Xn→ X almost surely and Xnhas the distribution function μn,n = 0,1,2,... We shall extend the Skorokhod representation theorem to the case where if there are a sequence of separable metric spaces Sn,a sequence of probability measures μnand a sequence of measurable mappings n such that μnn-1w→μ0,then there exist a probability space(Ω,F,P) and Sn-valued random elements Xndefined on Ω,with distribution μnand such that n(Xn) → X0 almost surely. In addition,we present several applications of our result including some results in random matrix theory,while the original Skorokhod representation theorem is not applicable.
基金Project partially supported by the National Natural Science Foundation of ChinaTianyuan Mathematics Foundation.
文摘Weak convergence of Markov processes is studied by means of Dirichlet forms and two theorems for weak convergence of Hunt processes on general metric spaces are established.As applications,examples for weak convergence of symmetric or non symmetric Dirichlet processes on finite and infinite spaces are given.
基金Supported by the National Natural Science Foundation of China (Grant No. 11071053)the Natural Science Foundation of Hebei Province (Grant No. A.2010001482)the Project of Science and Research of Hebei Education Department (the second round in 2010)
文摘In this paper,we introduce a new iterative scheme for finding the common element of the set of solutions of an equilibrium problem,the set of solutions of variational inequalities for an α-inversely strongly monotone operator and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and 2-uniformly convex Banach space.Some weak convergence theorems are obtained,to extend the previous work.
基金Partially supported by the National Natural Science Foundation of China
文摘This paper considers diffusion processes {X^(?)(t)} on R^2, which are perturbations of dynamical system {X(t)} (dX(t)=b(X(t))dt) on R^2. By means of weak convergence of probability measures, the authors characterize the limit behavior for empirical measures of {X^(?)(t)} in a neighborhood domain of saddle point of the dynamical system as the perturbations tend to zero.
文摘The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generalized functions and the convergence is weak convergence in the sense of the convergence of continuous linear functionals defining them. The figures show that the approximations of the Fourier series possess oscillations around the function which they represent in a broad band embedding them. This is some analogue to the Gibbs phenomenon. A modification of Fourier series by expansion in powers cosn(x)for the symmetric part of functions and sin(x)cosn−1(x)for the antisymmetric part (analogous to Taylor series) is discussed and illustrated by examples. The Fourier series and their convergence behavior are illustrated also for some 2π-periodic delta-function-like sequences connected with the Poisson theorem showing non-vanishing oscillations around the singularities similar to the Gibbs phenomenon in the neighborhood of discontinuities of functions. .
文摘The almost convergent function which was introduced by Raimi [6] and discussed by Ho [4], Das and Nanda [2, 3], is the continuous analogue of almost convergent sequences （see [5]）. In this paper, we establish the Tauberian conditions and the Cauchy criteria for weak almost convergent functions on R2＋ .
基金Partially supported by NSFC(No.11701304)the K.C.Wong Education Foundation。
文摘In this paper we study the Freidlin-Wentzell's large deviation principle for the following nonlinear fractional stochastic heat equation driven by Gaussian noise∂/∂tu^(ε)=D_(δ)^(α)(t,x)+√εσ(u^(ε)(t,x))W(t,x),(t,x)∈[0,T]×R,where D_(δ)^(α)is a nonlocal fractional differential operator and W is the Gaussian noise which is white in time and behaves as a fractional Brownian motion with Hurst index H satisfying 3-α/4<H<1/2,in the space variable.The weak convergence approach plays an important role.
文摘Several results on iterative methods for equilibrium problems have been proposed and studied in the literature.Most of these results are obtained when the associated bifunction of the equilibrium problem is either a monotone or pseudomonotone operator.Results on iterative methods for equilibrium problems without monotonicity conditions on the bifunction are still few in the literature.In this paper,we study equilibrium problems for which the underlined bifunction is not assumed any form of monotonicity.We propose two weakly convergent iterative algorithms and one strongly convergent algorithm.We obtain our convergence results without assuming either monotonicity or pseudomonotonicity condition on the bifunction.Our proposed algorithms are tested numerically to be more efficient and faster than some few available algorithms for equilibrium problems without monotonicity in the literature.
