Commun. Korean Math. Soc. 2011; 26(3): 483-498
Printed September 1, 2011
https://doi.org/10.4134/CKMS.2011.26.3.483
Copyright © The Korean Mathematical Society.
Yeol Je Cho, Nawab Hussain, and Hemant Kumar Pathak
Gyeongsang National University, King Abdul Aziz University, Pt. Ravishankar Shukla University
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
2019; 34(2): 465-475
2018; 33(3): 767-786
2017; 32(4): 1009-1024
2017; 32(1): 39-46
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd