ξ-asymptotically uniformly smooth, ξ-asymptotically uniformly convex, and (β) operators

Asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces

This paper provides a fixed point theorem for asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces as well as new effective results on the Krasnosel’skiı̆–Mann iterations of such mappings. The latter were found using methods from logic and the paper continues a case study in the general program of extracting effective data from prima-facie ineffective proofs in the fixed po...

Three-space Property for Asymptotically Uniformly Smooth Renormings

We prove that if Y is a closed subspace of a Banach space X such that Y and X/Y admit an equivalent asymptotically uniformly smooth norm, then X also admits an equivalent asymptotically uniformly smooth norm. The proof is based on the use of the Szlenk index and yields a few other applications to renorming theory.

Convergence results‎: ‎A new type iteration scheme for two asymptotically nonexpansive mappings in uniformly convex Banach spaces

‎In this article‎, ‎we introduce a new type iterative scheme for‎ ‎approximating common fixed points of two asymptotically‎ ‎nonexpansive mappings is defined‎, ‎and weak and strong convergence‎ ‎theorem are proved for the new iterative scheme in a uniformly‎ ‎convex Banach space‎. ‎The results obtained in this article‎ ‎represent an extension as well as refinement of previous known‎ ‎resu...

Convergence of Implicit and Explicit Schemes for an Asymptotically Nonexpansive Mapping in q-Uniformly Smooth and Strictly Convex Banach Spaces

Weak convergence theorems for two asymptotically quasi-nonexpansive non-self mappings in uniformly convex Banach spaces

The purpose of this paper is to establish some weak convergence theorems of modified two-step iteration process with errors for two asymptotically quasi-nonexpansive non-self mappings in the setting of real uniformly convex Banach spaces if E satisfies Opial’s condition or the dual E∗ of E has the Kedec-Klee property. Our results extend and improve some known corresponding results from the exis...