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Convergence of an implicit iteration process with errors for two asymptotically nonexpansive mappings

100%

Temir S.

tom Vol. 46, nr 4

781--793

The purpose of this paper is to introduce an implicit iterative process with errors for approximating common fixed point of two finite families of asymptotically nonexpansive mappings in the framework of Banach space. The results presented in this paper extend and generalize the corresponding results of Qin et al. [Convergence analysis of implicit iterative algorithms for asymptotically nonexpansive mappings, Appl. Math. Comp. 210 (2009), 542–550], Thakur [Weak and strong convergence of composite implicititeration process, Appl. Math. Comp. 190 (2007), 965–973] and some others.

Structure of the fixed point set of asymptotically nonexpansive mappings in Banach spaces with weak uniformly normal structure

84%

Sahu D. R. , Agarwal R. P. , O'Regan D.

tom Vol. 17, nr 1

51-68

This paper is concerned with weak uniformly normal structure and the structure of the set of fixed points of Lipschitzian mappings. It is shown that in a Banach space X with weak uniformly normal structure, every asymptotically regular Lipschitzian semigroup of self-mappings defined on a weakly compact convex subset of X satisfies the (ω)-fixed point property. We show that if X has a uniformly Gâteaux differentiable norm, then the set of fixed points of every asymptotically nonexpansive mapping is nonempty and sunny nonexpansive retract of C. Our results improve several known fixed point theorems for the class of Lipschitzian mappings in a general Banach space.