In this paper, we prove that a family of self-maps {Ti,j}i,j∈N in 2-metric space has a unique common fixed point if （i） {Ti,j}i,j∈N satisfies the same type contractive condition for each j ∈ N; （ii） Tm,μ .Tn,v...In this paper, we prove that a family of self-maps {Ti,j}i,j∈N in 2-metric space has a unique common fixed point if （i） {Ti,j}i,j∈N satisfies the same type contractive condition for each j ∈ N; （ii） Tm,μ .Tn,v = Tn,v.Tm.μ for all m,n,μ,v ∈ N with μ≠v. Our main result generalizes and improves many known unique common fixed point theorems in 2-metric spaces.展开更多
In this paper, we introduce generalized cyclic C-contractions through p number of subsets of a probabilistic metric space and establish two fixed point results for such contractions. In our first theorem we use the Ha...In this paper, we introduce generalized cyclic C-contractions through p number of subsets of a probabilistic metric space and establish two fixed point results for such contractions. In our first theorem we use the Hadzic type t-norm. In our next theorem we use Lukasiewicz t-norm. Our results generalize the results of Choudhury and Bhandari [11]. A control function [3] has been utilized in our second theorem. The results are illustrated with some examples.展开更多
Generally,the classic iterative learning control(ILC)methods focus on finding design conditions for repetitive systems to achieve the perfect tracking of any specified trajectory,whereas they ignore a fundamental prob...Generally,the classic iterative learning control(ILC)methods focus on finding design conditions for repetitive systems to achieve the perfect tracking of any specified trajectory,whereas they ignore a fundamental problem of ILC:whether the specified trajectory is trackable,or equivalently,whether there exist some inputs for the repetitive systems under consideration to generate the specified trajectory?The current paper contributes to dealing with this problem.Not only is a concept of trackability introduced formally for any specified trajectory in ILC,but also some related trackability criteria are established.Further,the relation between the trackability and the perfect tracking tasks for ILC is bridged,based on which a new convergence analysis approach is developed for ILC by leveraging properties of a functional Cauchy sequence(FCS).Simulation examples are given to verify the effectiveness of the presented trackability criteria and FCS-induced convergence analysis method for ILC.展开更多
Abstract. We use the two mappings satisfying II-expansive conditions on complex valued metric spaces to construct the convergent sequences and prove that the unique limit of the sequences is the point of coincidence o...Abstract. We use the two mappings satisfying II-expansive conditions on complex valued metric spaces to construct the convergent sequences and prove that the unique limit of the sequences is the point of coincidence or common fixed point of the two mappings. Also, we discuss the uniqueness of points of coincidence or common fixed points and give the existence theorems of unique fixed points. The obtained results generalize and improve the corresponding conclusions in references.展开更多
In this paper, we establish the existence of the minimal Lp （p 〉 1） solution of backward stochastic differential equations （BSDEs） where the time horizon may be finite or infinite and the generators have a non-un...In this paper, we establish the existence of the minimal Lp （p 〉 1） solution of backward stochastic differential equations （BSDEs） where the time horizon may be finite or infinite and the generators have a non-uniformly linear growth with respect to t. The main idea is to construct a sequence of solutions {（Yn, Zn）} which is a Cauchy sequence in Sp × Mp space, and finally we prove {（Yn, Zn）} converges to the Lp （p 〉 1） solution of BSDEs.展开更多
Some topological properties of cone metric spaces are discussed and proved that every cone metric space （X, d） is complete if and only if every family of closed subsets of X which has the finite intersection propert...Some topological properties of cone metric spaces are discussed and proved that every cone metric space （X, d） is complete if and only if every family of closed subsets of X which has the finite intersection property and which for every c ε E, 0 〈〈 c contains a set of diameter less that c has non-empty intersection.展开更多
In this work, we introduce a few versions of Caristi’s fixed point theorems in G-cone metric spaces which extend Caristi’s fixed point theorems in metric spaces. Analogues of such fixed point theorems are proved in ...In this work, we introduce a few versions of Caristi’s fixed point theorems in G-cone metric spaces which extend Caristi’s fixed point theorems in metric spaces. Analogues of such fixed point theorems are proved in this space. Our work extends a good number of results in this area of research.展开更多
A backward stochastic diferential equation is discussed in this paper. Under some weaker conditions than uniformly Lipschitzian condition given by Pardoux and Peng(1990), using Picard interaction and Cauchy sequence, ...A backward stochastic diferential equation is discussed in this paper. Under some weaker conditions than uniformly Lipschitzian condition given by Pardoux and Peng(1990), using Picard interaction and Cauchy sequence, the existence and uniqueness of the solutions to the backward stochastic diferential equation.展开更多
文摘In this paper, we prove that a family of self-maps {Ti,j}i,j∈N in 2-metric space has a unique common fixed point if （i） {Ti,j}i,j∈N satisfies the same type contractive condition for each j ∈ N; （ii） Tm,μ .Tn,v = Tn,v.Tm.μ for all m,n,μ,v ∈ N with μ≠v. Our main result generalizes and improves many known unique common fixed point theorems in 2-metric spaces.
文摘In this paper, we introduce generalized cyclic C-contractions through p number of subsets of a probabilistic metric space and establish two fixed point results for such contractions. In our first theorem we use the Hadzic type t-norm. In our next theorem we use Lukasiewicz t-norm. Our results generalize the results of Choudhury and Bhandari [11]. A control function [3] has been utilized in our second theorem. The results are illustrated with some examples.
基金supported in part by the National Natural Science Foundation of China (62273018)in part by the Science and Technology on Space Intelligent Control Laboratory (HTKJ2022KL502006)。
文摘Generally,the classic iterative learning control(ILC)methods focus on finding design conditions for repetitive systems to achieve the perfect tracking of any specified trajectory,whereas they ignore a fundamental problem of ILC:whether the specified trajectory is trackable,or equivalently,whether there exist some inputs for the repetitive systems under consideration to generate the specified trajectory?The current paper contributes to dealing with this problem.Not only is a concept of trackability introduced formally for any specified trajectory in ILC,but also some related trackability criteria are established.Further,the relation between the trackability and the perfect tracking tasks for ILC is bridged,based on which a new convergence analysis approach is developed for ILC by leveraging properties of a functional Cauchy sequence(FCS).Simulation examples are given to verify the effectiveness of the presented trackability criteria and FCS-induced convergence analysis method for ILC.
基金supported by the National Natural Science Foundation of China (No. 11361064)
文摘Abstract. We use the two mappings satisfying II-expansive conditions on complex valued metric spaces to construct the convergent sequences and prove that the unique limit of the sequences is the point of coincidence or common fixed point of the two mappings. Also, we discuss the uniqueness of points of coincidence or common fixed points and give the existence theorems of unique fixed points. The obtained results generalize and improve the corresponding conclusions in references.
基金Supported by the National Natural Science Foundation of China(Grant No.11371362)the Fundamental Research Funds for the Central Universities(Grant No.2012LWB48)
文摘In this paper, we establish the existence of the minimal Lp （p 〉 1） solution of backward stochastic differential equations （BSDEs） where the time horizon may be finite or infinite and the generators have a non-uniformly linear growth with respect to t. The main idea is to construct a sequence of solutions {（Yn, Zn）} which is a Cauchy sequence in Sp × Mp space, and finally we prove {（Yn, Zn）} converges to the Lp （p 〉 1） solution of BSDEs.
基金Foundation item： Supported by tile National Natural Science Foundation of China（10971185, 10971186） Supported by the Research Fund for Higher Education of Fujian Province（JK2011031）
文摘Some topological properties of cone metric spaces are discussed and proved that every cone metric space （X, d） is complete if and only if every family of closed subsets of X which has the finite intersection property and which for every c ε E, 0 〈〈 c contains a set of diameter less that c has non-empty intersection.
文摘In this work, we introduce a few versions of Caristi’s fixed point theorems in G-cone metric spaces which extend Caristi’s fixed point theorems in metric spaces. Analogues of such fixed point theorems are proved in this space. Our work extends a good number of results in this area of research.
基金Supported by NNSF of China(10171010)Scientifc Research Fund of Zhejiang Provincial Education Department(Y201329578)
文摘A backward stochastic diferential equation is discussed in this paper. Under some weaker conditions than uniformly Lipschitzian condition given by Pardoux and Peng(1990), using Picard interaction and Cauchy sequence, the existence and uniqueness of the solutions to the backward stochastic diferential equation.
