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

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

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Article ID: iaor20134150
Volume: 56
Issue: 4
Start Page Number: 1563
End Page Number: 1589
Publication Date: Aug 2013
Journal: Journal of Global Optimization
Authors: ,
Keywords: global optimization, iterative methods, mapping, fixed point theory
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. (2010), Hao (2010), Jaiboon and Kumam (2010) and many others.

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