Convergence theorems for two viscosity iterative algorithms for solving equilibrium problems and fixed point problems

Journal article

Authors/Editors

POOM KUMAM

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Publication Details

Author list: Katchang P., Jaiboon C., Kumam P.

Publication year: 2011

Volume number: 72

Issue number: 2

Start page: 217

End page: 235

Number of pages: 19

ISSN: 1311-8080

eISSN: 1311-8080

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-80855141560&partnerID=40&md5=f9fdd627dfa1d2c6e426097be01b46b2

Languages: English-Great Britain (EN-GB)

Abstract

In this paper, we introduce two viscosity iterative algorithms for rinding the set of solution for equilibrium problems and fixed point problems in a Hilbert space. We show that the sequence converges strongly to a common element of the above two sets under some parameters controlling conditions. As applications, at the end of paper we utilize our results to study some convergence problem for strictly pseudocontractive mappings and rinding the zeros of maximal monotone operators. Our results are generalizations and extensions of the results of Yao and Liou [Iterative Algorithms for Nonexpansive Mapping, Fixed Point Theory and Applications, Volume 2008, Article ID 384629, 10 pages.] and Su and Li [Strong convergence theorems on two iterative method for non-expansive mappings, Applied Mathematics and Computation, 181, No. 1 (2006), 332-341.] and some recent results. ฉ 2011 Academic Publications, Ltd.

Keywords