Abstract
In this paper, we present a new extragradient algorithm for approximating a solution of the split equilibrium problems and split fixed point problems. The strong convergence theorems are proved in the framework of Hilbert spaces under some mild conditions. We apply the obtained main result for the problem of finding a solution of split variational inequality problems and split fixed point problems and a numerical example and computational results are also provided.
Highlights
Let C and D be nonempty closed and convex subsets of real Hilbert spaces H1 and H2, respectively, and let H1 and H2 be endowed with an inner product ·, · and the corresponding norm ·
In 2013, Anh [2] introduced an extragradient algorithm for finding a common element of fixed point set of a nonexpansive mapping and solution set of an equilibrium problem on pseudomonotone and Lipschitz-type continuous bifunction in real Hilbert space
Let C be a nonempty closed and convex subset of a real Hilbert space H and f : C × C → R be a bifunction, we will assume the following conditions: (A1) f is pseudomonotone on C and f (x, x) = 0 for all x ∈ C; (A2) f is weakly continuous on C × C in the sense that if x, y ∈ C and {xn}, {yn} ⊂ C
Summary
Let C and D be nonempty closed and convex subsets of real Hilbert spaces H1 and H2, respectively, and let H1 and H2 be endowed with an inner product ·, · and the corresponding norm ·. In 2013, Anh [2] introduced an extragradient algorithm for finding a common element of fixed point set of a nonexpansive mapping and solution set of an equilibrium problem on pseudomonotone and Lipschitz-type continuous bifunction in real Hilbert space.
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.
