Fixed point and weak convergence theorems for point-dependent λ-hybrid mappings in Banach spacesReportar como inadecuado




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Fixed Point Theory and Applications

, 2011:105

First Online: 23 December 2011Received: 25 August 2011Accepted: 23 December 2011

Abstract

The purpose of this article is to study the fixed point and weak convergence problem for the new defined class of point-dependent λ-hybrid mappings relative to a Bregman distance Df in a Banach space. We at first extend the Aoyama-Iemoto-Kohsaka-Takahashi fixed point theorem for λ-hybrid mappings in Hilbert spaces in 2010 to this much wider class of nonlinear mappings in Banach spaces. Secondly, we derive an Opial-like inequality for the Bregman distance and apply it to establish a weak convergence theorem for this new class of nonlinear mappings. Some concrete examples in a Hilbert space showing that our extension is proper are also given.

2010 MSC: 47H09; 47H10.

Keywordsfixed point Bregman distance Gâteaux differentiable subdifferential  Download fulltext PDF



Autor: Young-Ye Huang - Jyh-Chung Jeng - Tian-Yuan Kuo - Chung-Chien Hong

Fuente: https://link.springer.com/







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