A new general algorithm for set-valued mappings and equilibrium problem
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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
Keywords
- Equilibrium problem
- variational inequality
- set-valued mapping
- condition (E).
MSC
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