On modified Noor iterations for nonexpansive mappings

On modified Noor iterations for strongly pseudocontractive mappings

In this paper, we analyze a three-step iterative scheme for three strongly pseudocontractive mappings in a uniformly smooth Banach space. Our results can be viewed as an extension of three-step and two-step iterative schemes of Glowinski and Le Tallec [3], Noor [1215] and Ishikawa [7], Liu [10] and Xu [20]. 2000 Mathematics Subject Classification: Primary 47H10, 47H17: Secondary 54H25

Modified Noor iterations for infinite family of strict pseudo-contraction mappings

Strong convergence of modified Noor iterations

A point x ∈ C is a fixed point of T provided Tx = x. Denote by F(T) the set of fixed points of T ; that is, F(T)= {x ∈ C : Tx = x}. It is assumed throughout the paper that T is a nonexpansive mapping such that F(T) =∅. One classical way to study nonexpansive mappings is to use contractions to approximate a nonexpansive mapping [1, 9]. More precisely, take t ∈ (0,1) and define a contraction Tt :...

Modified Noor Iterations for Infinite Family of Strict Pseudo-contraction Mappings

We introduce a modified Noor iteration scheme generated by an infinite family of strict pseudo-contractive mappings and prove the strong convergence theorems of the scheme in the framework of q−uniformly smooth and strictly convex Banach space. Results shown here are extensions and refinements of previously known results.

Bounds on Iterations of Asymptotically Quasi-nonexpansive Mappings

This paper establishes explicit quantitative bounds on the computation of approximate fixed points of asymptotically (quasi-) nonexpansive mappings f by means of iterative processes. Here f : C → C is a selfmapping of a convex subset C ⊆ X of a uniformly convex normed space X . We consider general Krasnoselski-Mann iterations with and without error terms. As a consequence of our quantitative an...