Abstract
AbstractWe consider a new iterative algorithm for finding a common element of the set of generalized mixed equilibrium problems, the set of solutions of a system of quasivariational inclusions for two difference inverse strongly accretive operators, and common set of fixed points for strict pseudo-contraction mappings in Banach spaces. Furthermore, strong convergence theorems of this method were established under suitable assumptions imposed on the algorithm parameters. The results obtained in this paper improve and extend some results in the literature.
Highlights
Equilibrium theory represents an important area of mathematical sciences such as optimization, operations research, game theory, financial mathematics, and mechanics
The important generalization of variational inequalities, called variational inclusions, have been extensively studied and generalized in different directions to study a wide class of problems arising in mechanics, optimization, nonlinear programming, economics, finance, and applied sciences
Katchang and Kumam 30, further extended the work of 26 and constructed a viscosity iterative scheme for finding solutions of a general system of variational inequalities 1.22 for two inverse-strongly accretive operators with a viscosity of modified extragradient methods and solutions of fixed point problems involving the nonexpansive mapping in Banach spaces
Summary
Equilibrium theory represents an important area of mathematical sciences such as optimization, operations research, game theory, financial mathematics, and mechanics. Katchang and Kumam 30 , further extended the work of 26 and constructed a viscosity iterative scheme for finding solutions of a general system of variational inequalities 1.22 for two inverse-strongly accretive operators with a viscosity of modified extragradient methods and solutions of fixed point problems involving the nonexpansive mapping in Banach spaces. In this paper, motivated by the above results and the iterative schemes considered in Qin et al 31, 32 and Katchang and Kumam 30 , we present a new general iterative scheme so call a relaxed extragradient-type method for finding a common element of the set of solutions for generalized mixed equilibrium problems, the set of solutions of common system of variational inclusions for two inverse-strongly accretive operators and common set of fixed points for a strict pseudocontraction in 2-uniformly smooth Banach spaces. The results presented in this paper extend and improve the results of Qin et al 31, 32 and many authors
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