• Title/Summary/Keyword: uniformly pointwise R-subweakly commuting mappings

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

  • Cho, Yeol-Je;Hussain, Nawab;Pathak, Hemant Kumar
    • Communications of the Korean Mathematical Society
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    • v.26 no.3
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    • pp.483-498
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    • 2011
  • 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.