In this works, by using the modified viscosity approximation method associated with Meir-Keeler contractions, we proved the convergence theorem for solving the fixed point problem of a nonexpansive semigroup and gener...In this works, by using the modified viscosity approximation method associated with Meir-Keeler contractions, we proved the convergence theorem for solving the fixed point problem of a nonexpansive semigroup and generalized mixed equilibrium problems in Hilbert spaces.展开更多
In this paper, we introduce some new classes of the totally quasi-G-asymptotically nonexpansive mappings and the totally quasi-G-asymptotically nonexpansive semigroups. Then, with the generalized f-projection operator...In this paper, we introduce some new classes of the totally quasi-G-asymptotically nonexpansive mappings and the totally quasi-G-asymptotically nonexpansive semigroups. Then, with the generalized f-projection operator, we prove some strong convergence theorems of a new modified Halpern type hybrid iterative algorithm for the totally quasi-G-asymptotically nonexpansive semigroups in Banach space. The results presented in this paper extend and improve some corresponding ones by many others.展开更多
Throughout this paper, we introduce a new hybrid iterative algorithm for finding a common element of the set of common fixed points of a finite family of uniformly asymptotically nonexpansive semigroups and the set of...Throughout this paper, we introduce a new hybrid iterative algorithm for finding a common element of the set of common fixed points of a finite family of uniformly asymptotically nonexpansive semigroups and the set of solutions of an equilibrium problem in the framework of Hilbert spaces. We then prove the strong convergence theorem with respect to the proposed iterative algorithm. Our results in this paper extend and improve some recent known results.展开更多
The internal Zappa-Szép products emerge when a semigroup has the property that every element has a unique decomposition as a product of elements from two given subsemigroups. The external version constructed from...The internal Zappa-Szép products emerge when a semigroup has the property that every element has a unique decomposition as a product of elements from two given subsemigroups. The external version constructed from actions of two semigroups on one another satisfying axiom derived by G. Zappa. We illustrate the correspondence between the two versions internal and the external of Zappa-Szép products of semigroups. We consider the structure of the internal Zappa-Szép product as an enlargement. We show how rectangular band can be described as the Zappa-Szép product of a left-zero semigroup and a right-zero semigroup. We find necessary and sufficient conditions for the Zappa-Szép product of regular semigroups to again be regular, and necessary conditions for the Zappa-Szép product of inverse semigroups to again be inverse. We generalize the Billhardt λ-semidirect product to the Zappa-Szép product of a semilattice E and a group G by constructing an inductive groupoid.展开更多
A general approach to transference principles for discrete and continuous sequence of operators (semi) groups is described. This allows one to recover the classical transference results of Calderon, Coifman and Weiss ...A general approach to transference principles for discrete and continuous sequence of operators (semi) groups is described. This allows one to recover the classical transference results of Calderon, Coifman and Weiss and of Berkson, Gilleppie and Muhly and the more recent one of the author. The method is applied to derive a new transference principle for (discrete and continuous) the sequence of operators semigroups that need not be grouped. As an application, functional calculus estimates for bounded sequence of operators with at most polynomially growing powers are derived, leading to a new proof of classical results by Peller from 1982. The method allows for a generalization of his results away from Hilbert spaces to -spaces and—involving the concept of γ-boundedness—to general spaces. Analogous results for strongly-continuous one-parameter (semi) groups are presented as well by Markus Haase [1]. Finally, an application is given to singular integrals for one-parameter semigroups.展开更多
We find the necessary and sufficient conditions on a coproduct of connected acts over a semigroup to be strongly hopfian. From this, we deduce the conditions of the strong hopfness for unitary acts over groups. Moreov...We find the necessary and sufficient conditions on a coproduct of connected acts over a semigroup to be strongly hopfian. From this, we deduce the conditions of the strong hopfness for unitary acts over groups. Moreover, we prove that a finite coproduct of strongly hopfian acts over an arbitrary semigroup is strongly hopfian.展开更多
The α-times integrated C semigroups, α > 0, are introduced and analyzed. The Laplace inverse transformation for α-times integrated C semigroups is obtained, some known results are generalized.
The infinite generator of α-times Integrated C semigroups and the properties of resolvent are given. At the same time, we discuss the relationship between the existence of strong solution of a class of nonhomogeneous...The infinite generator of α-times Integrated C semigroups and the properties of resolvent are given. At the same time, we discuss the relationship between the existence of strong solution of a class of nonhomogeneous abstract Cauchy problem and α-times integrated C semigroups, and a sufficient and necessary condition is obtained.展开更多
In this paper we prove the analyticity of the semigroups generated by some singular differential matrix operators of the form in the Banach space with suitable boundary conditions. To illustrate the work an example is...In this paper we prove the analyticity of the semigroups generated by some singular differential matrix operators of the form in the Banach space with suitable boundary conditions. To illustrate the work an example is discussed.展开更多
In this paper,the definitions of fuzzy regular subsemigroup and fuzzy left(right,intra-)regular sub-semigroup in semigroups are introduced.Some characterizations of them are given.Proposition 2.1.A fuzzy set A in a se...In this paper,the definitions of fuzzy regular subsemigroup and fuzzy left(right,intra-)regular sub-semigroup in semigroups are introduced.Some characterizations of them are given.Proposition 2.1.A fuzzy set A in a semigroup S is a fuzzy subsemigroup iff for any λ∈[0,1],if A_λ={x∈S|A(x)≥λ}≠ ,then A_λ is a subsemigroup of S.Proposition 2.2.A fuzzy set A in a semigroup S is a fuzzy left(right)ideal iff for any λ∈(0,1],if A={x∈S|A(x)展开更多
Let C be a closed bounded convex subset of a uniformaly convex Banach space X with a Frechet differentiable norm, F= {T(t):t ≥0} an asymptotically noncxpansivc semigroup on C, and u:[0,∞)→ C an almost-orbit of F. T...Let C be a closed bounded convex subset of a uniformaly convex Banach space X with a Frechet differentiable norm, F= {T(t):t ≥0} an asymptotically noncxpansivc semigroup on C, and u:[0,∞)→ C an almost-orbit of F. Then we show that {u(t):t ≥ 0} is almost convergent weakly to a common fixed point y of F, that isweak - lim1/tdr - y uniformly in s≥ 0.This implies that {u(t):t≥ 0} converges weakly to y if and onlyif u is weakly asymptotically regular, i.e lim (u(t + s) - u(t) = 0 weakly for all s≥ 0.展开更多
In this paper we are interested in studying the dissipativity of degenerate mixed differential operators involving an interface point. We show that, under particular interface conditions, such operators generate analy...In this paper we are interested in studying the dissipativity of degenerate mixed differential operators involving an interface point. We show that, under particular interface conditions, such operators generate analytic semigroups on an appropriate Hilbert space . To illustrate the results an example is discussed.展开更多
We establish that the Laplas operator with perturbation by symmetrised linear hall of displacement argument operators is the generator of unitary group in the Hilbert space of square integrable functions. The represen...We establish that the Laplas operator with perturbation by symmetrised linear hall of displacement argument operators is the generator of unitary group in the Hilbert space of square integrable functions. The representation of semigroup of Cauchy problem solutions for considered functional differential equation is given by the Feynman formulas.展开更多
This paper considers the differentiability of C 0 semigroups with respect to (w.r.t.) parameters contained in their infinitesimal generators.It is proved that the generalized continuity and strong differentiability ...This paper considers the differentiability of C 0 semigroups with respect to (w.r.t.) parameters contained in their infinitesimal generators.It is proved that the generalized continuity and strong differentiability of their infinitesimal generators w.r.t.parameters imply the differentiability of the C 0 semigroups.The results are applied to the differentiability of the solution of a linear delay differential equation w.r.t.its delays.展开更多
In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and （gener...In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and （generalized） bi-ideals, and also by the properties of their fuzzy left ideals, fuzzy right ideals and fuzzy （generalized） bi-ideals.展开更多
In this paper, author abtains a group of characteristic conditions for the infinitesimal generators of positive contraction semigroups and stochastic semigroups.Furthermore, Applications of them to linear transport th...In this paper, author abtains a group of characteristic conditions for the infinitesimal generators of positive contraction semigroups and stochastic semigroups.Furthermore, Applications of them to linear transport theory are discussed.展开更多
In this paper,we shall prove that for any positive interger n,there exists non-trivialcommutative finite semigroup of idempotent consisting of some n×n real quaternion matri-ces which is lower semilattice.In the ...In this paper,we shall prove that for any positive interger n,there exists non-trivialcommutative finite semigroup of idempotent consisting of some n×n real quaternion matri-ces which is lower semilattice.In the process of solving this problem we shall see thatmany properties of generalized inverses for complex matrices still hold for quaternions ma-展开更多
In his paper “On quasi-separative ‘semigroup’s’”, Krasilnikova, Yu. I. and Novikov, B. V. have studied congruences induced by certain relations on a “semigroup”. They further showed that if the “semigroup” is...In his paper “On quasi-separative ‘semigroup’s’”, Krasilnikova, Yu. I. and Novikov, B. V. have studied congruences induced by certain relations on a “semigroup”. They further showed that if the “semigroup” is quasi separative then the induced congruence is a semilattice congruence. In this paper we continue the study of these relations and the induced congruences i.e., the congruences induced by certain relations on ‘‘semigroup’s”. In this paper mainly it is observed that if S is a quasi-separative and regular “semigroup” then the necessary and sufficient condition for to be the smallest semilattice congruence η is obtained.展开更多
We introduce the concepts of unitary, almost unitary and strongly almost unitary subset of an ordered semigroup. For the notions of almost unitary and strongly almost unitary subset of an ordered semigroup, we use the...We introduce the concepts of unitary, almost unitary and strongly almost unitary subset of an ordered semigroup. For the notions of almost unitary and strongly almost unitary subset of an ordered semigroup, we use the notion of translational hull of an ordered semigroup. If (S,⋅,≤) is an ordered semigroup having an element e such that e ≤ e<sup>2</sup> and U is a nonempty subset of S such that u ≤ eu, u ≤ ue for all u ∈ U, we show that U is almost unitary in S if and only if U is unitary in . Also if (S,⋅,≤) is an ordered semigroup, e ∉ S, U is a nonempty subset of S, S<sup>e</sup>:= S ∪ {e} and U<sup>e</sup>:= U ∪ {e}, we give conditions that an (“extension” of S) ordered semigroup and the subset U<sup>e</sup> of S<sup>e</sup> must satisfy in order for U to be almost unitary or strongly almost unitary in S (in case U is strongly almost unitary in S, then the given conditions are equivalent).展开更多
We study types of boundedness of a semigroup on a Banach space in terms of the Cesáro-average and the behavior of the resolvent at the origin and also exhibit a characterization of type Hille-Yosida for the gener...We study types of boundedness of a semigroup on a Banach space in terms of the Cesáro-average and the behavior of the resolvent at the origin and also exhibit a characterization of type Hille-Yosida for the generators of ϕ<sup>j</sup>-bounded strongly continuous semigroups. Furthermore, these results are used to investigate the effect of the Perturbation on the type of the growth of sequences.展开更多
文摘In this works, by using the modified viscosity approximation method associated with Meir-Keeler contractions, we proved the convergence theorem for solving the fixed point problem of a nonexpansive semigroup and generalized mixed equilibrium problems in Hilbert spaces.
文摘In this paper, we introduce some new classes of the totally quasi-G-asymptotically nonexpansive mappings and the totally quasi-G-asymptotically nonexpansive semigroups. Then, with the generalized f-projection operator, we prove some strong convergence theorems of a new modified Halpern type hybrid iterative algorithm for the totally quasi-G-asymptotically nonexpansive semigroups in Banach space. The results presented in this paper extend and improve some corresponding ones by many others.
文摘Throughout this paper, we introduce a new hybrid iterative algorithm for finding a common element of the set of common fixed points of a finite family of uniformly asymptotically nonexpansive semigroups and the set of solutions of an equilibrium problem in the framework of Hilbert spaces. We then prove the strong convergence theorem with respect to the proposed iterative algorithm. Our results in this paper extend and improve some recent known results.
文摘The internal Zappa-Szép products emerge when a semigroup has the property that every element has a unique decomposition as a product of elements from two given subsemigroups. The external version constructed from actions of two semigroups on one another satisfying axiom derived by G. Zappa. We illustrate the correspondence between the two versions internal and the external of Zappa-Szép products of semigroups. We consider the structure of the internal Zappa-Szép product as an enlargement. We show how rectangular band can be described as the Zappa-Szép product of a left-zero semigroup and a right-zero semigroup. We find necessary and sufficient conditions for the Zappa-Szép product of regular semigroups to again be regular, and necessary conditions for the Zappa-Szép product of inverse semigroups to again be inverse. We generalize the Billhardt λ-semidirect product to the Zappa-Szép product of a semilattice E and a group G by constructing an inductive groupoid.
文摘A general approach to transference principles for discrete and continuous sequence of operators (semi) groups is described. This allows one to recover the classical transference results of Calderon, Coifman and Weiss and of Berkson, Gilleppie and Muhly and the more recent one of the author. The method is applied to derive a new transference principle for (discrete and continuous) the sequence of operators semigroups that need not be grouped. As an application, functional calculus estimates for bounded sequence of operators with at most polynomially growing powers are derived, leading to a new proof of classical results by Peller from 1982. The method allows for a generalization of his results away from Hilbert spaces to -spaces and—involving the concept of γ-boundedness—to general spaces. Analogous results for strongly-continuous one-parameter (semi) groups are presented as well by Markus Haase [1]. Finally, an application is given to singular integrals for one-parameter semigroups.
文摘We find the necessary and sufficient conditions on a coproduct of connected acts over a semigroup to be strongly hopfian. From this, we deduce the conditions of the strong hopfness for unitary acts over groups. Moreover, we prove that a finite coproduct of strongly hopfian acts over an arbitrary semigroup is strongly hopfian.
文摘The α-times integrated C semigroups, α > 0, are introduced and analyzed. The Laplace inverse transformation for α-times integrated C semigroups is obtained, some known results are generalized.
文摘The infinite generator of α-times Integrated C semigroups and the properties of resolvent are given. At the same time, we discuss the relationship between the existence of strong solution of a class of nonhomogeneous abstract Cauchy problem and α-times integrated C semigroups, and a sufficient and necessary condition is obtained.
文摘In this paper we prove the analyticity of the semigroups generated by some singular differential matrix operators of the form in the Banach space with suitable boundary conditions. To illustrate the work an example is discussed.
文摘In this paper,the definitions of fuzzy regular subsemigroup and fuzzy left(right,intra-)regular sub-semigroup in semigroups are introduced.Some characterizations of them are given.Proposition 2.1.A fuzzy set A in a semigroup S is a fuzzy subsemigroup iff for any λ∈[0,1],if A_λ={x∈S|A(x)≥λ}≠ ,then A_λ is a subsemigroup of S.Proposition 2.2.A fuzzy set A in a semigroup S is a fuzzy left(right)ideal iff for any λ∈(0,1],if A={x∈S|A(x)
文摘Let C be a closed bounded convex subset of a uniformaly convex Banach space X with a Frechet differentiable norm, F= {T(t):t ≥0} an asymptotically noncxpansivc semigroup on C, and u:[0,∞)→ C an almost-orbit of F. Then we show that {u(t):t ≥ 0} is almost convergent weakly to a common fixed point y of F, that isweak - lim1/tdr - y uniformly in s≥ 0.This implies that {u(t):t≥ 0} converges weakly to y if and onlyif u is weakly asymptotically regular, i.e lim (u(t + s) - u(t) = 0 weakly for all s≥ 0.
文摘In this paper we are interested in studying the dissipativity of degenerate mixed differential operators involving an interface point. We show that, under particular interface conditions, such operators generate analytic semigroups on an appropriate Hilbert space . To illustrate the results an example is discussed.
文摘We establish that the Laplas operator with perturbation by symmetrised linear hall of displacement argument operators is the generator of unitary group in the Hilbert space of square integrable functions. The representation of semigroup of Cauchy problem solutions for considered functional differential equation is given by the Feynman formulas.
文摘This paper considers the differentiability of C 0 semigroups with respect to (w.r.t.) parameters contained in their infinitesimal generators.It is proved that the generalized continuity and strong differentiability of their infinitesimal generators w.r.t.parameters imply the differentiability of the C 0 semigroups.The results are applied to the differentiability of the solution of a linear delay differential equation w.r.t.its delays.
基金The NSF(10961014) of Chinathe NSF(0501332) of Guangdong Province+1 种基金the Excellent Youth Talent Foundation(2009SQRZ149) of Anhui Provincethe Fuyang Normal College Youth Foundation (2008LQ11)
文摘In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and （generalized） bi-ideals, and also by the properties of their fuzzy left ideals, fuzzy right ideals and fuzzy （generalized） bi-ideals.
文摘In this paper, author abtains a group of characteristic conditions for the infinitesimal generators of positive contraction semigroups and stochastic semigroups.Furthermore, Applications of them to linear transport theory are discussed.
文摘In this paper,we shall prove that for any positive interger n,there exists non-trivialcommutative finite semigroup of idempotent consisting of some n×n real quaternion matri-ces which is lower semilattice.In the process of solving this problem we shall see thatmany properties of generalized inverses for complex matrices still hold for quaternions ma-
文摘In his paper “On quasi-separative ‘semigroup’s’”, Krasilnikova, Yu. I. and Novikov, B. V. have studied congruences induced by certain relations on a “semigroup”. They further showed that if the “semigroup” is quasi separative then the induced congruence is a semilattice congruence. In this paper we continue the study of these relations and the induced congruences i.e., the congruences induced by certain relations on ‘‘semigroup’s”. In this paper mainly it is observed that if S is a quasi-separative and regular “semigroup” then the necessary and sufficient condition for to be the smallest semilattice congruence η is obtained.
文摘We introduce the concepts of unitary, almost unitary and strongly almost unitary subset of an ordered semigroup. For the notions of almost unitary and strongly almost unitary subset of an ordered semigroup, we use the notion of translational hull of an ordered semigroup. If (S,⋅,≤) is an ordered semigroup having an element e such that e ≤ e<sup>2</sup> and U is a nonempty subset of S such that u ≤ eu, u ≤ ue for all u ∈ U, we show that U is almost unitary in S if and only if U is unitary in . Also if (S,⋅,≤) is an ordered semigroup, e ∉ S, U is a nonempty subset of S, S<sup>e</sup>:= S ∪ {e} and U<sup>e</sup>:= U ∪ {e}, we give conditions that an (“extension” of S) ordered semigroup and the subset U<sup>e</sup> of S<sup>e</sup> must satisfy in order for U to be almost unitary or strongly almost unitary in S (in case U is strongly almost unitary in S, then the given conditions are equivalent).
文摘We study types of boundedness of a semigroup on a Banach space in terms of the Cesáro-average and the behavior of the resolvent at the origin and also exhibit a characterization of type Hille-Yosida for the generators of ϕ<sup>j</sup>-bounded strongly continuous semigroups. Furthermore, these results are used to investigate the effect of the Perturbation on the type of the growth of sequences.
