Approximation of nearest common fixed points of asymptotically $I$-nonexpansive mappings in Banach spaces
Commun. Korean Math. Soc. 2011 Vol. 26, No. 3, 483-498
Printed September 1, 2011
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
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