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 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 https://doi.org/10.4134/CKMS.2011.26.3.483Published online 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 Full-Text :