A System of Generalized Mixed Equilibrium Problems, Maximal Monotone Operators, and Fixed Point Problems with Application to Optimization Problems | Zendy

Pongsakorn Sunthrayuth | Zendy; Poom Kumam | Zendy

Open Access

A System of Generalized Mixed Equilibrium Problems, Maximal Monotone Operators, and Fixed Point Problems with Application to Optimization Problems

Author(s) -

Pongsakorn Sunthrayuth,

Poom Kumam

Publication year - 2011

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2012/316276

Subject(s) - mathematics , monotone polygon , strongly monotone , fixed point , bounded function , element (criminal law) , operator (biology) , set (abstract data type) , iterative method , monotonic function , inverse , mathematical optimization , discrete mathematics , mathematical analysis , computer science , biochemistry , chemistry , geometry , repressor , political science , transcription factor , law , gene , programming language

We introduce a new iterative algorithm for finding a common element of the set of solutions of a system of generalized mixed equilibrium problems, zero set of the sum of a maximal monotone operators and inverse-strongly monotone mappings, and the set of common fixed points of an infinite family of nonexpansive mappings with infinite real number. Furthermore, we prove under some mild conditions that the proposed iterative algorithm converges strongly to a common element of the above four sets, which is a solution of the optimization problem related to a strongly positive bounded linear operator. The results presented in the paper improve and extend the recent ones announced by many others

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