Abstract
For the purpose of this paper, we use the method different from the relaxed extragradient method for finding a common element of the set of fixed points of a quasi-nonexpansive mapping, the set of solutions of equilibrium problems, and the set of solutions of a modified system of variational inequalities without demiclosed condition of W and $W_{\omega}:= (1-\omega )I+\omega W$ , where W is a quasi-nonexpansive mapping and $\omega\in (0,\frac{1}{2} )$ in the framework of Hilbert space. By using our main result, we obtain a strong convergence theorem involving a finite family of nonspreading mappings and another corollary. Moreover, we give a numerical example to encourage our main theorem.
Highlights
Let C be a nonempty closed convex subset of a real Hilbert space H
Let be a bifunction of C × C into R, where R is the set of real numbers
After we investigated Theorem . , Theorem . and researchers in the same direction, we have the questions as follows: ( ) Can we prove strong convergence theorem without demiclosed condition and
Summary
Let C be a nonempty closed convex subset of a real Hilbert space H. Many strong convergence theorems of quasi-nonexpansive mapping W were proved by assuming the following conditions: Many authors used the extragradient method to prove fixed point theorem of nonlinear mappings.
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.
