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

Title & Authors
APPROXIMATION OF NEAREST COMMON FIXED POINTS OF ASYMPTOTICALLY I-NONEXPANSIVE MAPPINGS IN BANACH SPACES
Cho, Yeol-Je; Hussain, Nawab; Pathak, Hemant Kumar;

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$\small{\^{a}}$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$\small{\^{a}}$ateaux differentiable norm;uniform normal structure;
Language
English
Cited by
1.
Strong convergence theorems for uniformly L-Lipschitzian asymptotically pseudocontractive mappings in Banach spaces, Journal of Inequalities and Applications, 2013, 2013, 1, 79
2.
On Unification of the Strong Convergence Theorems for a Finite Family of Total Asymptotically Nonexpansive Mappings in Banach Spaces, Journal of Applied Mathematics, 2012, 2012, 1
3.
Best proximity points of non-self mappings, TOP, 2013, 21, 2, 287
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