In this paper, we investigate the validity of approximation theorm of K. Fan for a demicompact 1-set-contraction map defined on a closed ball,an annulus and a sphere in cones. From this, we improve all recent results ...In this paper, we investigate the validity of approximation theorm of K. Fan for a demicompact 1-set-contraction map defined on a closed ball,an annulus and a sphere in cones. From this, we improve all recent results of Lin [2]. As applications of our theorems, we discuss the existence of positive solutions to twopoint boundary value-problems of differential equations in Banach space. At the same time, the recent main results of (3) established by Guo Dajun are Generalized and supplemented.展开更多
In this paper,applying the concept of generalized KKM map,we study problems of variational inequalities.We weaken convexity(concavity)conditions for a functional of two variables ■(x,y)in the general variational ineq...In this paper,applying the concept of generalized KKM map,we study problems of variational inequalities.We weaken convexity(concavity)conditions for a functional of two variables ■(x,y)in the general variational inequalities.Last,we show a proof of non-topological degree meth- od of acute angle principle about monotone operator as an application of these results.展开更多
In this paper, Jurgen's relative result is extended to a uniformly convex Banach space, and the convergence of iterative sequence in an uniformly convex Banach space for asymptotically non-expansive mapping is ...In this paper, Jurgen's relative result is extended to a uniformly convex Banach space, and the convergence of iterative sequence in an uniformly convex Banach space for asymptotically non-expansive mapping is proved.展开更多
In this work, the authors introduce the concept of(p, q)-quasi-contraction mapping in a cone metric space. We prove the existence and uniqueness of a fixed point for a(p, q)-quasi-contraction mapping in a complete con...In this work, the authors introduce the concept of(p, q)-quasi-contraction mapping in a cone metric space. We prove the existence and uniqueness of a fixed point for a(p, q)-quasi-contraction mapping in a complete cone metric space. The results of this paper generalize and unify further fixed point theorems for quasi-contraction, convex contraction mappings and two-sided convex contraction of order 2.展开更多
Let E be a real Banach space and K be a nonempty closed convex and bounded subset of E. Let Ti ： K→ K, i=1, 2,... ,N, be N uniformly L-Lipschitzian, uniformly asymptotically regular with sequences {ε^（i）n} and as...Let E be a real Banach space and K be a nonempty closed convex and bounded subset of E. Let Ti ： K→ K, i=1, 2,... ,N, be N uniformly L-Lipschitzian, uniformly asymptotically regular with sequences {ε^（i）n} and asymptotically pseudocontractive mappings with sequences {κ^（i）n}, where {κ^（i）n} and {ε^（i）n}, i = 1, 2,... ,N, satisfy certain mild conditions. Let a sequence {xn} be generated from x1 ∈ K by zn：= （1-μn）xn＋μnT^nnxn, xn＋1 ：= λnθnx1＋ [1 - λn（1 ＋ θn）]xn ＋ λnT^nnzn for all integer n ≥ 1, where Tn = Tn（mod N）, and {λn}, {θn} and {μn} are three real sequences in [0, 1] satisfying appropriate conditions. Then ｜｜xn- Tixn｜｜→ 0 as n→∞ for each l ∈ {1, 2,..., N}. The results presented in this paper generalize and improve the corresponding results of Chidume and Zegeye, Reinermann, Rhoades and Schu.展开更多
文摘In this paper, we investigate the validity of approximation theorm of K. Fan for a demicompact 1-set-contraction map defined on a closed ball,an annulus and a sphere in cones. From this, we improve all recent results of Lin [2]. As applications of our theorems, we discuss the existence of positive solutions to twopoint boundary value-problems of differential equations in Banach space. At the same time, the recent main results of (3) established by Guo Dajun are Generalized and supplemented.
文摘In this paper,applying the concept of generalized KKM map,we study problems of variational inequalities.We weaken convexity(concavity)conditions for a functional of two variables ■(x,y)in the general variational inequalities.Last,we show a proof of non-topological degree meth- od of acute angle principle about monotone operator as an application of these results.
文摘In this paper, Jurgen's relative result is extended to a uniformly convex Banach space, and the convergence of iterative sequence in an uniformly convex Banach space for asymptotically non-expansive mapping is proved.
文摘In this work, the authors introduce the concept of(p, q)-quasi-contraction mapping in a cone metric space. We prove the existence and uniqueness of a fixed point for a(p, q)-quasi-contraction mapping in a complete cone metric space. The results of this paper generalize and unify further fixed point theorems for quasi-contraction, convex contraction mappings and two-sided convex contraction of order 2.
基金Foundation item： the National Natural Science Foundation of China （No. 10771141） the Natural Science Foundation of Zhejiang Province （Y605191） the Natural Science Foundation of Heilongjiang Province （No. A0211） and the Scientific Research Foundation from Zhejiang Province Education Committee （No. 20051897）.
文摘Let E be a real Banach space and K be a nonempty closed convex and bounded subset of E. Let Ti ： K→ K, i=1, 2,... ,N, be N uniformly L-Lipschitzian, uniformly asymptotically regular with sequences {ε^（i）n} and asymptotically pseudocontractive mappings with sequences {κ^（i）n}, where {κ^（i）n} and {ε^（i）n}, i = 1, 2,... ,N, satisfy certain mild conditions. Let a sequence {xn} be generated from x1 ∈ K by zn：= （1-μn）xn＋μnT^nnxn, xn＋1 ：= λnθnx1＋ [1 - λn（1 ＋ θn）]xn ＋ λnT^nnzn for all integer n ≥ 1, where Tn = Tn（mod N）, and {λn}, {θn} and {μn} are three real sequences in [0, 1] satisfying appropriate conditions. Then ｜｜xn- Tixn｜｜→ 0 as n→∞ for each l ∈ {1, 2,..., N}. The results presented in this paper generalize and improve the corresponding results of Chidume and Zegeye, Reinermann, Rhoades and Schu.
