ON THE CONVERGENCE OF AN ITERATION PROCESS FOR TOTALLY ASYMPTOTICALLY I-NONEXPANSIVE MAPPINGS
Keywords:
Totally Asymptotically I-Nonexpansive Mapping, Total Asymptotically Nonexpansive Mapping, Opial Condition, (A′) Condition, Strong and weak convergence, Common fixed pointAbstract
Suppose that K be a nonempty closed convex subset of a real Banach space X and T,S:K???K be two totally asymptotically I-nonexpansive mappings, where I:K???K is a totally asymptotically nonexpansive mapping. We define the iterative sequence {x_{n}} by
{<K1.1/>,n??????,???
<K1.1 ilk="MATRIX" >x??????Kx_{n+1}=(1-??_{n})x_{n}+??_{n}S?เธขย?y_{n}y_{n}=(1-??_{n})x_{n}+??_{n}T?เธขย?z_{n}z_{n}=(1-??_{n})x_{n}+??_{n}I?เธขย?x_{n}</K1.1>where {??_{n}},{??_{n}} ve {??_{n}} are sequences in [0,1].Under some suitable conditions, the strong and weak convergence theorems of {x_{n}} to a common fixed point of S,T and I are obtained.
Additional Files
Published
Issue
Section
License
Copyright (c) 2024 Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO)
![Creative Commons License](http://i.creativecommons.org/l/by-nc-nd/4.0/88x31.png)
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Copyright (c) 2010 Journal of Nonlinear Analysis and Optimization: Theory & Applications
This work is licensed under aย Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.