T h e homotopic invariance of fixed points of set-valued contractions and nonexpansive mappings is studied. As application, nonlinear alternative principles are given. A LeraySchauder alternative and an antipodal theorem for set-valued nonexpansive mappings are also included.

a definition of two jointly asymptotically nonexpansive mappings s and t on uniformly convex banach space e is studied to approximate common fixed points of two such mappings through weak and strong convergence of an ishikawa type iteration scheme generated by s and t on a bounded closed and convex subset of e. as a consequence of the notion of two jointly asymptotically nonexpansive maps, we c...

In 1916, Tricomi 1 introduced originally the concept of quasi-nonexpansive for real functions. Subsequently, this concept has studied for mappings in Banach and metric spaces see, e.g., 2–7 . Recently, some generalized types of quasi-nonexpansive mappings in metric and Banach spaces have appeared. For example, see Ahmed and Zeyada 8 , Qihou 9–11 and others. Unless stated to the contrary, we ass...

* Correspondence: changss@yahoo. cn; [email protected] Department of Mathematics, Yibin university, Yibin, Sichuan 644007, China Department of Mathematics, College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China Full list of author information is available at the end of the article Abstract The purpose of this article is to introduc...

for all x, y ∈ C and each n ≥ 1. The class of asymptotically nonexpansive mappings was introduced by Goebel and Kirk [1] as an important generalization of nonexpansive mappings. It was proved in [1] that if C is a nonempty bounded closed convex subset of a real uniformly convex Banach space and T is an asymptotically nonexpansive self mapping on C, then F (T ) is nonempty closed convex subset o...

Abstract In a real Banach space, let the VI indicate variational inclusion for two accretive operators and CFPP denote common fixed point problem of countably many nonexpansive mappings. this article, we introduce generalized extragradient implicit method solving general system inequalities (GSVI) with constraints. Strong convergence suggested to solution GSVI constraints under some suitable as...