AN ITERATIVE SCHEME FOR GENERALIZED EQUILIBRIUM, VARIATIONAL INEQUALITY AND FIXED POINT PROBLEMS BASED ON THE EXTRA GRADIENT METHOD

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JAHEDI S.; PAYVAND M.A.

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Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2016 | Volume:2 | Issue:7 Page(s): 61-76

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Title

AN ITERATIVE SCHEME FOR GENERALIZED EQUILIBRIUM, VARIATIONAL INEQUALITY AND FIXED POINT PROBLEMS BASED ON THE EXTRA GRADIENT METHOD

Author(s)

JAHEDI S. | PAYVAND M.A. | Issue Writer Certificate

Keywords

EQUILIBRIUM PROBLEMQ1

VARIATIONAL INEQUALITYQ1

FIXED POINT PROBLEMQ1

STRICTLY PSEUDO CONTRACTION MAPPINGQ1

Abstract

The problem of generalized EQUILIBRIUM PROBLEM is very general in the different subjects. Optimization problems, variational inequalities, Nash EQUILIBRIUM PROBLEM and minimax problems are as special cases of generalized EQUILIBRIUM PROBLEM. The purpose of this paper is to investigate the problem of approximating a common element of the set of generalized EQUILIBRIUM PROBLEM, VARIATIONAL INEQUALITY problem and FIXED POINT PROBLEM. In this article, a new iterative algorithm is introduced based on theextragradient method. Under suitable conditions, a weak convergence theorem for finding a common solution of a generalized EQUILIBRIUM PROBLEM, a VARIATIONAL INEQUALITY problem and the set of fixed points of a finite family of STRICTLY PSEUDO CONTRACTION MAPPINGs is proved. Our results improve and generalize some recent results in the literature. Finally, we give a numerical example to show the validity of the results.

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APA: Copy

JAHEDI, S., & PAYVAND, M.A.. (2016). AN ITERATIVE SCHEME FOR GENERALIZED EQUILIBRIUM, VARIATIONAL INEQUALITY AND FIXED POINT PROBLEMS BASED ON THE EXTRA GRADIENT METHOD. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 2(7), 61-76. SID. https://sid.ir/paper/257304/en

Vancouver: Copy

JAHEDI S., PAYVAND M.A.. AN ITERATIVE SCHEME FOR GENERALIZED EQUILIBRIUM, VARIATIONAL INEQUALITY AND FIXED POINT PROBLEMS BASED ON THE EXTRA GRADIENT METHOD. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2016;2(7):61-76. Available from: https://sid.ir/paper/257304/en

IEEE: Copy

S. JAHEDI, and M.A. PAYVAND, “AN ITERATIVE SCHEME FOR GENERALIZED EQUILIBRIUM, VARIATIONAL INEQUALITY AND FIXED POINT PROBLEMS BASED ON THE EXTRA GRADIENT METHOD,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 2, no. 7, pp. 61–76, 2016, [Online]. Available: https://sid.ir/paper/257304/en

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