An iterative algorithm for common fixed points for nonexpansive semigroups and strictly pseudo-contractive mappings with optimization problems

Phayap Katchang () and Poom Kumam ()

Journal of Global Optimization, 2013, vol. 56, issue 4, 1563-1589

Abstract: In this paper, we introduce an iterative algorithm for finding a common element of the set of solutions of a system of mixed equilibrium problems, the set of solutions of a variational inclusion problems for inverse strongly monotone mappings, the set of common fixed points for nonexpansive semigroups and the set of common fixed points for an infinite family of strictly pseudo-contractive mappings in Hilbert spaces. Furthermore, we prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm under some suitable conditions which solves some optimization problems. Our results extend and improve the recent results of Chang et al. (Appl Math Comput 216:51–60, 2010 ), Hao (Appl Math Comput 217(7):3000–3010, 2010 ), Jaiboon and Kumam (Nonlinear Anal 73:1180–1202, 2010 ) and many others. Copyright Springer Science+Business Media, LLC. 2013

Keywords: System of mixed equilibrium problem; Variational inclusion; Optimization problems; Nonexpansive mapping; Nonexpansive semigroups; Infinite family of strictly pseudo-contractive mappings; η-strongly convex functions; Metric projection; 47H09; 47H10; 47H17; 47J20; 49J30; 49J40; 49M05; 90C99 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10898-012-9927-y

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