Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2011; 26(3): 483-498

Printed September 1, 2011

https://doi.org/10.4134/CKMS.2011.26.3.483

Copyright © The Korean Mathematical Society.

Approximation of nearest common fixed points of asymptotically $I$-nonexpansive mappings in Banach spaces

Yeol Je Cho, Nawab Hussain, and Hemant Kumar Pathak

Gyeongsang National University, King Abdul Aziz University, Pt. Ravishankar Shukla University

Abstract

In this paper, we introduce a new class of uniformly pointwise $R$-subweakly commuting self-mappings and prove several common fixed point theorems and best approximation results for uniformly pointwise $R$-subweakly commuting asymptotically $I$-nonexpansive mappings in normed linear spaces. We also establish some results concerning strong convergence of nearest common fixed points of asymptotically $I$-non\-expansive mappings in reflexive Banach spaces with a uniformly G\^{a}teaux differentiable norm. Our results unify and generalize various known results given by some authors to a more general class of noncommuting mappings.

Keywords: uniformly pointwise $R$-subweakly commuting mappings, uniformly $R$-subweakly commuting mappings, asymptotically $I$-nonexpansive mappings, Banach operator pair, strong convergence, G\^{a}teaux differentiable norm, uniform normal structure

MSC numbers: 47H10, 54H25