# APPROXIMATION OF NEAREST COMMON FIXED POINTS OF ASYMPTOTICALLY I-NONEXPANSIVE MAPPINGS IN BANACH SPACES

• Cho, Yeol-Je (Department of Mathematics Education and the RINS Gyeongsang National University) ;
• Hussain, Nawab (Department of Mathematics King Abdul Aziz University) ;
• Pathak, Hemant Kumar (School of Studies in Mathematics Pt. Ravishankar Shukla University)
• Received : 2010.04.10
• Published : 2011.07.31

#### Abstract

In this paper, we introduce a new class of uniformly point-wise R-subweakly commuting self-mappings and prove several common fixed point theorems and best approximation results for uniformly point-wise 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.

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