Abstract
We introduce two iterative sequence for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a countable family of strict pseudocontractions in Hilbert Space. Then we study the weak and strong convergence of the sequences.
Highlights
Let C be a nonempty closed convex subset of a Hilbert space H and let T be a self-mapping of C
1.1 if 1.1 holds, we say that T is a κ-strict pseudocontraction
Thanks to the condition introduced by Aoyama et al 5, We introduce two iterative sequence for finding a common element of the set of solutions of an equilibrium problems and the set of fixed points of a countable family of strict pseudocontractions mappings in Hilbert Space
Summary
Let C be a nonempty closed convex subset of a Hilbert space H and let T be a self-mapping of C. Takahashi 4 introduced an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of the equilibrium problem and the set of fixed points of a nonexpansive mapping in Hilbert spaces. They studied the strong convergence of the sequences generated by their algorithm for a solution of the EP which is a fixed point of a nonexpansive mapping defined on a closed convex subset of a Hilbert space. Thanks to the condition introduced by Aoyama et al 5 , We introduce two iterative sequence for finding a common element of the set of solutions of an equilibrium problems and the set of fixed points of a countable family of strict pseudocontractions mappings in Hilbert Space. The additional condition is inspired by Marino and Xu 6 and Kim and Xu 7
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
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 call
