This article introduces the concept of commutative semigroups of almost asymptotically nonexpansive-type mappings in a Banach space X which has the Opial property and whose norm is UKK, and establishes the weak conver...This article introduces the concept of commutative semigroups of almost asymptotically nonexpansive-type mappings in a Banach space X which has the Opial property and whose norm is UKK, and establishes the weak convergence theorems for almostorbits of this class of commutative semigroups. The author improves, extends and develops some recent and earlier results.展开更多
A new class of almost asymptotically nonexpansive type mappings in Banach spaces is introduced,which includes a number of known classes of nonlinear Lipschitzian mappings and non_Lipschitzian mappings in Banach spaces...A new class of almost asymptotically nonexpansive type mappings in Banach spaces is introduced,which includes a number of known classes of nonlinear Lipschitzian mappings and non_Lipschitzian mappings in Banach spaces as special cases; for example,the known classes of nonexpansive mappings,asymptotically nonexpansive mappings and asymptotically nonexpansive type mappings.The convergence problem of modified Ishikawa iterative sequences with errors for approximating fixed points of almost asymptotically nonexpansive type mappings is considered.Not only S.S.Chang's inequality but also H.K.Xu's one for the norms of Banach spaces are applied to make the error estimate between the exact fixed point and the approximate one.Moreover,Zhang Shi_sheng's method(Applied Mathematics and Mechanics(English Edition),2001,22(1):25-34) for making the convergence analysis of modified Ishikawa iterative sequences with errors is extended to the case of almost asymptotically nonexpansive type mappings. The new convergence criteria of modified Ishikawa iterative sequences with errors for finding fixed points of almost asymptotically nonexpansive type mappings in uniformly convex Banach spaces are presented. Also,the new convergence criteria of modified Mann iterative sequences with errors for this class of mappings are immediately obtained from these criteria.The above results unify,improve and generalize Zhang Shi_sheng's ones on approximating fixed points of asymptotically nonexpansive type mappings by the modified Ishikawa and Mann iterative sequences with errors.展开更多
The purpose of this paper is to study a new two-step iterative scheme with mean errors of mixed type for two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappings and prove str...The purpose of this paper is to study a new two-step iterative scheme with mean errors of mixed type for two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappings and prove strong convergence theorems for the new two-step iterative scheme in uniformly convex Banach spaces.展开更多
In this paper, relaxed iterative algorithms of Krasnoselskii-type and Halpern-type that approximate a solution of a system of a generalized mixed equilibrium problem anda common fixed point of a countable family of to...In this paper, relaxed iterative algorithms of Krasnoselskii-type and Halpern-type that approximate a solution of a system of a generalized mixed equilibrium problem anda common fixed point of a countable family of totally quasi-C-asymptotically nonexpansivemulti-valued maps are constructed. Strong convergence of the sequence generated by thesealgorithms is proved in uniformly smooth and strictly convex real Banach spaces with Kadec-Klee property. Furthermore, several applications of our theorems are also presented. Finally,our theorems are significant improvements on several important recent results for this classof nonlinear problems.展开更多
Let X be a uniformly convex Banach space X such that its dual X^＊ has the KK property. Let C be a nonempty bounded closed convex subset of X and G be a directed system. Let ={Tt ： t ∈ G} be a family of asymptotica...Let X be a uniformly convex Banach space X such that its dual X^＊ has the KK property. Let C be a nonempty bounded closed convex subset of X and G be a directed system. Let ={Tt ： t ∈ G} be a family of asymptotically nonexpansive type mappings on C. In this paper, we investigate the asymptotic behavior of {Ttx0 ： t∈ G} and give its weak convergence theorem.展开更多
Let C be a nonempty weakly compact convex subset of a Banach space X,and T:C→C a mapping of asymptotically nonexpansive type.Then there hold the following conclusions:(i)if X has uniform normal structure and lim sup ...Let C be a nonempty weakly compact convex subset of a Banach space X,and T:C→C a mapping of asymptotically nonexpansive type.Then there hold the following conclusions:(i)if X has uniform normal structure and lim sup j→∞|||T^jN|||<√N(X),where |||T^j(N)||| is the exact Lipschitz constant of T^jN,N is some positive integer,and N(X)is the normal structure coefficient of X,then T has a fixed point;(ii) if X is uniformly convex in every direction and has weak uniform normal structure,then T has a fixed point.展开更多
τ是X的一个线性H ausdorff拓扑,在一致τ-O p ia l或τ-UKK条件下,给出了渐近非扩张型映照的不动点定理.由于L1(μ)并不具备通常的O p ia l条件,但是在L1(μ)赋予抽象测度拓扑τ下,(X,τ)满足一致τ-O p ia条l件,从而给出L1(μ)中渐近...τ是X的一个线性H ausdorff拓扑,在一致τ-O p ia l或τ-UKK条件下,给出了渐近非扩张型映照的不动点定理.由于L1(μ)并不具备通常的O p ia l条件,但是在L1(μ)赋予抽象测度拓扑τ下,(X,τ)满足一致τ-O p ia条l件,从而给出L1(μ)中渐近非扩张型映照的不动点定理.展开更多
基金Project supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE,P.R.C., by the Dawn Program Foundation in Shanghai, and by Shanghai Leading Academic Discipline Project Fund (T0401).
文摘This article introduces the concept of commutative semigroups of almost asymptotically nonexpansive-type mappings in a Banach space X which has the Opial property and whose norm is UKK, and establishes the weak convergence theorems for almostorbits of this class of commutative semigroups. The author improves, extends and develops some recent and earlier results.
文摘A new class of almost asymptotically nonexpansive type mappings in Banach spaces is introduced,which includes a number of known classes of nonlinear Lipschitzian mappings and non_Lipschitzian mappings in Banach spaces as special cases; for example,the known classes of nonexpansive mappings,asymptotically nonexpansive mappings and asymptotically nonexpansive type mappings.The convergence problem of modified Ishikawa iterative sequences with errors for approximating fixed points of almost asymptotically nonexpansive type mappings is considered.Not only S.S.Chang's inequality but also H.K.Xu's one for the norms of Banach spaces are applied to make the error estimate between the exact fixed point and the approximate one.Moreover,Zhang Shi_sheng's method(Applied Mathematics and Mechanics(English Edition),2001,22(1):25-34) for making the convergence analysis of modified Ishikawa iterative sequences with errors is extended to the case of almost asymptotically nonexpansive type mappings. The new convergence criteria of modified Ishikawa iterative sequences with errors for finding fixed points of almost asymptotically nonexpansive type mappings in uniformly convex Banach spaces are presented. Also,the new convergence criteria of modified Mann iterative sequences with errors for this class of mappings are immediately obtained from these criteria.The above results unify,improve and generalize Zhang Shi_sheng's ones on approximating fixed points of asymptotically nonexpansive type mappings by the modified Ishikawa and Mann iterative sequences with errors.
文摘The purpose of this paper is to study a new two-step iterative scheme with mean errors of mixed type for two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappings and prove strong convergence theorems for the new two-step iterative scheme in uniformly convex Banach spaces.
文摘In this paper, relaxed iterative algorithms of Krasnoselskii-type and Halpern-type that approximate a solution of a system of a generalized mixed equilibrium problem anda common fixed point of a countable family of totally quasi-C-asymptotically nonexpansivemulti-valued maps are constructed. Strong convergence of the sequence generated by thesealgorithms is proved in uniformly smooth and strictly convex real Banach spaces with Kadec-Klee property. Furthermore, several applications of our theorems are also presented. Finally,our theorems are significant improvements on several important recent results for this classof nonlinear problems.
基金Foundation item： the National Natural Science Foundation of China （No. 10571150） the Natural Science Foundation of Jiangsu Education Committee of China （No. 07KJB110131） and the Natural Science Foundation of Yangzhou University （No. FK0513101）.
文摘Let X be a uniformly convex Banach space X such that its dual X^＊ has the KK property. Let C be a nonempty bounded closed convex subset of X and G be a directed system. Let ={Tt ： t ∈ G} be a family of asymptotically nonexpansive type mappings on C. In this paper, we investigate the asymptotic behavior of {Ttx0 ： t∈ G} and give its weak convergence theorem.
基金This research is supported both by the Teaching Research Award Fund tor Outstanding Young Teachers in Higher Education Institutions of MOE, P. R. C., by the Dawn Program Fund in Shanghai.
文摘Let C be a nonempty weakly compact convex subset of a Banach space X,and T:C→C a mapping of asymptotically nonexpansive type.Then there hold the following conclusions:(i)if X has uniform normal structure and lim sup j→∞|||T^jN|||<√N(X),where |||T^j(N)||| is the exact Lipschitz constant of T^jN,N is some positive integer,and N(X)is the normal structure coefficient of X,then T has a fixed point;(ii) if X is uniformly convex in every direction and has weak uniform normal structure,then T has a fixed point.
文摘τ是X的一个线性H ausdorff拓扑,在一致τ-O p ia l或τ-UKK条件下,给出了渐近非扩张型映照的不动点定理.由于L1(μ)并不具备通常的O p ia l条件,但是在L1(μ)赋予抽象测度拓扑τ下,(X,τ)满足一致τ-O p ia条l件,从而给出L1(μ)中渐近非扩张型映照的不动点定理.
