Viscosity Approximation Methods for Zeros of Accretive Operators and Fixed Point Problems in Banach Spaces

Journal article

Authors/Editors

POOM KUMAM

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Publication Details

Author list: Sunthrayuth P., Cho Y.J., Kumam P.

Publisher: Springer

Publication year: 2016

Journal: Bulletin of the Malaysian Mathematical Sciences Society (0126-6705)

Volume number: 39

Issue number: 2

Start page: 773

End page: 793

Number of pages: 21

ISSN: 0126-6705

eISSN: 2180-4206

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84960396449&doi=10.1007%2fs40840-015-0139-8&partnerID=40&md5=8fde896fd99351d768122656ff285721

Languages: English-Great Britain (EN-GB)

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Abstract

In this paper, we introduce iterative algorithms for finding a zero of set-valued accretive operators by the viscosity approximation method based on Meir–Keeler-type contractions in a reflexive Banach space which admits a weakly continuous duality mapping. We obtain some strong convergence theorems under suitable conditions. As applications, we apply our results for finding common fixed point of nonexpansive semigroups and for solving equilibrium problem, optimization problem, and variational inequalities. © 2015, Malaysian Mathematical Sciences Society and Universiti Sains Malaysia.

Keywords

Meir–Keeler-type contraction