A new general algorithm for set-valued mappings and equilibrium problem


Authors

Javad Vahidi - Department of Mathematics, Iran University of Science and Technology, Tehran, Iran.


Abstract

We consider a multi-step algorithm to approximate a common element of the set of solutions of monotone and Lipschitz-type continuous equilibrium problems, and the set of common fixed points of a finite family of set-valued mappings satisfying condition (E). We prove strong convergence theorems of such an iterative scheme in real Hilbert spaces. This common solution is the unique solution of a variational inequality problem and it satisfies the optimality condition for a minimization problem. The main result extends various results exiting in the literature.


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ISRP Style

Javad Vahidi, A new general algorithm for set-valued mappings and equilibrium problem, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 3, 1103--1115

AMA Style

Vahidi Javad, A new general algorithm for set-valued mappings and equilibrium problem. J. Nonlinear Sci. Appl. (2016); 9(3):1103--1115

Chicago/Turabian Style

Vahidi, Javad. "A new general algorithm for set-valued mappings and equilibrium problem." Journal of Nonlinear Sciences and Applications, 9, no. 3 (2016): 1103--1115


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