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

Temir S.

Demonstratio Mathematica

2013

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

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

Journal of Applied Analysis

2011

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.

Strong and weak convergence of implicit iterative process with errors for asymptotically nonexpansive mappings

Gu F.

Journal of Applied Analysis

2006

Vol. 12, nr 2

267-282

The purpose of this paper is to study the weak and strong convergence of an new implicit iteration process to a common fixed point for a finite family of asymptotically nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve important known results in [1], [2], [4]-[9], [11]-[15] and others.

Strong convergence of approximants to fixed points of asymptotically nonexpansive mappings in Banach spaces without uniform convexity

Sahu D. R., Jung J. S., Cho Y. J.

Demonstratio Mathematica

2004

Vol. 37, nr 2

419--428