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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.

Strict pseud-contraction strong convergence theorems for strict pseud-contractions

Qin X., Su Y.

Journal of Mathematics and Applications

2008

Vol. 30

137-149

In this paper, we prove two strong convergence theorems for strict pseudocontractions in Hilbert spaces by hybrid methods. Our results extend and improve the recent ones announced by Nakajo and Takahashi [K. Nakajo, W. Takahashi,. Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003), 372-379], Marino and Xu [G. Marino, H.K. Xu, Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, J. Math. Anal. Appl. 329 (2007), 336-346], Martinez-Yanes and Xu [C. Martinez-Yanes, H.K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anai. 64 (2006), 2400-2411] and some others.

Approximation of common fixed points of a family of asymptotically quasi-nonexpansive mappings

Sahu D., Shrivastava S., Malager B.

Demonstratio Mathematica

2008

Vol. 41, nr 3

651-659

In this paper, we study the convergence of the sequence of Ishikawa iteration of rank-r to common fixed points of a finite family of asymptotically quasi-nonexpansive mappings in uniformly convex Banach spaces. Our results extend and improve some known recent results.