Two block hybrid projection method for solving a common solution for a system of generalized equilibrium problems and fixed point problems for two countable families

Two block hybrid projection method for solving a common solution for a system of generalized equilibrium problems and fixed point problems for two countable families

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Article ID: iaor2014275
Volume: 7
Issue: 8
Start Page Number: 1745
End Page Number: 1763
Publication Date: Dec 2013
Journal: Optimization Letters
Authors: ,
Keywords: iterative methods, projection algorithms, Banach space
Abstract:

In this paper, we introduce a new iterative sequence which is constructed by using the new modified two block hybrid projection method for solving the common solution problem for a system of generalized equilibrium problems of inverse strongly monotone mappings and a system of bifunctions satisfying certain conditions, and the common fixed point problems for families of uniformly quasi ‐ ϕ equ1 ‐ asymptotically nonexpansive and locally uniformly Lipschitz continuous. Strong convergence theorems are proved on approximating a common solution of a system of generalized equilibrium problems and fixed point problems for two countable families in Banach spaces. Our results presented in this paper improve and extend many recent results in this area.

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