New algorithms for solving system of generalized mixed equilibrium problems and some nonlinear problems, with applications

In this paper, new iterative algorithms of Krasnoselkii-type and Halpern-type for approximating common fixed points of a countable family of equally continuous and totally quasi-φ-asymptotically nonexpansive maps, common zeros of a countable family of -inverse strongly monotone maps and a common ele...

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Bibliographic Details
Published in:Optimization Vol. 67; no. 12; pp. 2325 - 2345
Main Authors: Nnyaba, U. V., Romanus, O. M.
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis 02.12.2018
Taylor & Francis LLC
Subjects:
Algorithms
Banach spaces
equally continuous maps
Fixed points (mathematics)
Halpern-type algorithm
Iterative algorithms
Iterative methods
Krasnoselskii-type algorithm
system of generalized mixed equilibrium problems
totally quasi-φ-asymptotically nonexpansive multi-valued maps
ISSN:0233-1934, 1029-4945
Online Access:Get full text
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Summary:In this paper, new iterative algorithms of Krasnoselkii-type and Halpern-type for approximating common fixed points of a countable family of equally continuous and totally quasi-φ-asymptotically nonexpansive maps, common zeros of a countable family of -inverse strongly monotone maps and a common element of a set of solutions to a system of generalized mixed equilibrium problems in a 2-uniformly convex and uniformly smooth real Banach space are introduced and studied. Our theorems are significant improvements of some recent important results, in particular, the results of Deng (J Fixed Point Theory appl. 2016); Ofoedu and Malonza (Appl Math Comput. 2011;217:6019-6030), and Wang et al. (Fixed Point Theory Appl. 2012;34).
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2018.1542530