Abstract
We introduce a new iterative scheme for finding the common element of the set of solutions of the generalized equilibrium problems, the set of fixed points of an infinite family of nonexpansive mappings, and the set of solutions of the variational inequality problems for a relaxed -cocoercive and -Lipschitz continuous mapping in a real Hilbert space. Then, we prove the strong convergence of a common element of the above three sets under some suitable conditions. Our result can be considered as an improvement and refinement of the previously known results.
Highlights
Variational inequalities introduced by Stampacchia 1 in the early sixties have had a great impact and influence in the development of almost all branches of pure and applied sciences
It is well known that the variational inequalities are equivalent to the fixed point problems
It is well known that the convergence of a projection method requires the operator to be strongly monotone and Lipschitz continuous
Summary
Variational inequalities introduced by Stampacchia 1 in the early sixties have had a great impact and influence in the development of almost all branches of pure and applied sciences. Qin et al 6 introduced an iterative scheme for finding a common fixed points of a finite family of nonexpansive mappings, the set of solutions of the variational inequality problem for a relaxed cocoercive mapping, and the set of solutions of the equilibrium problems in a real Hilbert space. In this paper, motivated by iterative schemes considered in 1.15 , 1.25 , and 1.26 we will introduce a new iterative process 3.4 below for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings, the set of solutions of the generalized equilibrium problem, and the set of solutions of variational inequality problem for a relaxed u, v -cocoercive mapping in a real Hilbert space.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
