Strong Convergence Theorems of a New General Iterative Process with Meir-Keeler Contractions for a Countable Family of -Strict Pseudocontractions in -Uniformly Smooth Banach Spaces

Yanlai Song,Changsong Hu

doi:10.1155/2010/354202

Yanlai Song, Changsong Hu

Open Access

https://doi.org/10.1155/2010/354202

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Abstract

We introduce a new iterative scheme with Meir-Keeler contractions for strict pseudocontractions in -uniformly smooth Banach spaces. We also discuss the strong convergence theorems for the new iterative scheme in -uniformly smooth Banach space. Our results improve and extend the corresponding results announced by many others.

Highlights

Throughout this paper, we denote by E and E∗ a real Banach space and the dual space of E, respectively
We show the uniqueness of a solution of the variational inequality 2.3
We prove that x∗ solves the variational inequality 2.3

Summary

Introduction

Throughout this paper, we denote by E and E∗ a real Banach space and the dual space of E, respectively. Where Ti is non-self-λi-strictly pseudocontraction, f is a contraction and A is a strong positive linear bounded operator in Banach space. 1.12 xn 1 αnγ φ xn γnxn 1 − γn I − αnA yn, n ≥ 1, where Tn is non-self λn-strictly pseudocontraction, φ is a MKC contraction and A is a strong positive linear bounded operator in Banach space.

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Conclusion