Sezgin Akbulut

An iteration process for common xed points of two nonself asymptotically nonexpansive mappings

Abstract In this paper, we introduce an iteration process for approximating common fixed points of two nonself asymptotically nonexpansive map- pings in Banach spaces. Our process contains Mann iteration process and some other processes for nonself mappings but is independent of Ishikawa iteration process. We prove some weak and strong convergence theorems for this iteration process. Our results generalize and improve some results in contemporary literature.

On the subclass of p-valently functions

Using the Salagean derivative, we introduce and study a class of p-valently functions with negative coefficients. Coefficients estimates, distortion theorems, and extreme points for this class are given. The results presented here extends many known results.

A fixed point theorem for multivalued maps in hyperconvex spaces

Bugajewski [Math. Comput. Modell. 32 (2000) 1457] extend the Baillion fixed point theorem from [Contemporary Math. Am. Math. Soc. 72 (1988) 11]. In this paper, we proved a version of Bugajewskis theorem for multivalued maps defined on a bounded hyperconvex subset of a normed space.

STRONG AND Δ-CONVERGENCE OF A FASTER ITERATION PROCESS IN HYPERBOLIC SPACE

Abstract. In this article, we first give metric version of an iterationscheme of Agarwal et al. [1] and approximate fixed points of two finitefamilies of nonexpansive mappings in hyperbolic spaces through this iter-ation scheme which is independent of but faster than Mann and Ishikawascheme. Also we consider case of three finite families of nonexpansivemappings. But, we need an extra condition to get convergence. Our con-vergence theorems generalize and refine many know results in the currentliterature. 1. IntroductionThroughout the article, Ndenotes the set of positive integers and I denotesthe set of first N natural numbers. Let (X,d) be a metric space and K bea nonempty subset of X. A selfmap T on K is said to be nonexpansive ifd(Tx,Ty) ≤ d(x,y). Denote by F (T) the set of fixed points of T and byF = ∩ Ni=1 (F (T i ) ∩F (S i )) the set of common fixed points of two finite familiesof mappings {T i : i ∈ I} and {S i : i ∈ I}.We know that Mann and Ishikawa iteration processes are defined for givenx

Convergence Theorems on a New Iteration Process for Two Asymptotically Nonexpansive Nonself-Mappings with Errors in Banach Spaces

We introduce a new two-step iterative scheme for two asymptotically nonexpansive nonself-mappings in a uniformly convex Banach space. Weak and strong convergence theorems are established for this iterative scheme in a uniformly convex Banach space. The results presented extend and improve the corresponding results of Chidume et al. (2003), Wang (2006), Shahzad (2005), and Thianwan (2008).

Convergence theorems for a family of multivalued nonexpansive mappings in hyperbolic spaces

Abstract In this article we modify an iteration process to prove strong convergence and Δ— convergence theorems for a finite family of nonexpansive multivalued mappings in hyperbolic spaces. The results presented here extend some existing results in the literature.