General iterative methods for common fixed points of asymptotically nonexpansive mappings

Godwin Chidi Ugwunnadi

doi:10.30755/NSJOM.10799

General iterative methods for common fixed points of asymptotically nonexpansive mappings

Godwin Chidi Ugwunnadi^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we study an iterative process for approx-imating a common fixed point of afamily of uniformly asymptotically regular asymptotically nonexpansive mappings with variational inequality problem in uniformly convex Banach space with uniformly Gâteaux differentiable norm. We prove a strong convergence theorem under some suitable conditions. Our result is applicable in L_p(ℓ_p) spaces, 1 < p < ∞ (and consequently in Sobolev spaces). Our results improve and general-ize some well-known results in the literature.

Original language	English
Pages (from-to)	47-74
Number of pages	28
Journal	Novi Sad Journal of Mathematics
Volume	51
Issue number	2
DOIs	https://doi.org/10.30755/NSJOM.10799
Publication status	Published - 2021
Externally published	Yes

Keywords

Asymptotically non-expansive mapping
Fixed point
Variational inequality
µ-strictly pseudocontractive mapping
η-strongly accretive maps

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10.30755/NSJOM.10799

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abstract = "In this paper, we study an iterative process for approx-imating a common fixed point of afamily of uniformly asymptotically regular asymptotically nonexpansive mappings with variational inequality problem in uniformly convex Banach space with uniformly G{\^a}teaux differentiable norm. We prove a strong convergence theorem under some suitable conditions. Our result is applicable in Lp(ℓp) spaces, 1 < p < ∞ (and consequently in Sobolev spaces). Our results improve and general-ize some well-known results in the literature.",

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AB - In this paper, we study an iterative process for approx-imating a common fixed point of afamily of uniformly asymptotically regular asymptotically nonexpansive mappings with variational inequality problem in uniformly convex Banach space with uniformly Gâteaux differentiable norm. We prove a strong convergence theorem under some suitable conditions. Our result is applicable in Lp(ℓp) spaces, 1 < p < ∞ (and consequently in Sobolev spaces). Our results improve and general-ize some well-known results in the literature.

KW - Asymptotically non-expansive mapping

KW - Fixed point

KW - Variational inequality

KW - µ-strictly pseudocontractive mapping

KW - η-strongly accretive maps

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SP - 47

EP - 74

JO - Novi Sad Journal of Mathematics

JF - Novi Sad Journal of Mathematics

IS - 2

ER -

General iterative methods for common fixed points of asymptotically nonexpansive mappings

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Keywords

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