Abstract
We introduce a new iterative scheme for finding a common element of the solutions sets of a finite family of equilibrium problems and fixed points sets of an infinite family of nonexpansive mappings in a Hilbert space. As an application, we solve a multiobjective optimization problem using the result of this paper.
Highlights
Let H be a Hilbert space and C be a nonempty, closed, and convex subset of H
Let Φ be a bifunction of C × C into R, where R is the set of real numbers
Many problems arising from physics, optimization, and economics can reduce to finding a solution of an equilibrium problem
Summary
Let H be a Hilbert space and C be a nonempty, closed, and convex subset of H. Takahashi 1 first introduced an iterative scheme by the viscosity approximation method for finding a common element of the solutions set of equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. Let C be a nonempty closed and convex subset of a Hilbert space H, {Tn}∞n 1 : H → H be a countable family of nonexpansive mappings, and {Φi}mi 1 : C × C → R be m bifunctions satisfying conditions A1 – A4 such that Ω. 1. we prove that the iterative process {xn} defined by 1.10 strongly converge to an element x∗ ∈ Ω, which is the unique solution of the variational inequality. As an application of our main result, we solve a multiobjective optimization problem
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
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.
