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DOI QR Code

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

Cho, Yeol-Je;Hussain, Nawab;Pathak, Hemant Kumar

  • 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.

Keywords

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

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