Abstract
We introduce a new method for a system of generalized equilibrium problems, system of variational inequality problems, and fixed point problems by using -mapping generated by a finite family of nonexpansive mappings and real numbers. Then, we prove a strong convergence theorem of the proposed iteration under some control condition. By using our main result, we obtain strong convergence theorem for finding a common element of the set of solution of a system of generalized equilibrium problems, system of variational inequality problems, and the set of common fixed points of a finite family of strictly pseudocontractive mappings.
Highlights
Let H be a real Hilbert space, and let C be a nonempty closed convex subset of H
A mapping T of H into itself is called nonexpansive if T x − T y ≤ x − y for all x, y ∈ H
Goebel and Kirk 1 showed that F T is always closed convex, and nonempty provided T has a bounded trajectory
Summary
Let H be a real Hilbert space, and let C be a nonempty closed convex subset of H. Many iterative methods are purposed for finding a common element of the solutions of the equilibrium problem and fixed point problem of nonexpansive mappings, see 8–10. In 2010, Qin, et al 12 introduced a iterative scheme method for finding a common element of EP F1, A , EP F2, B and common fixed point of infinite family of nonexpansive mappings. They defined {xn} in the following way: x1 ∈ C, arbitrarily; F1 un, u.
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.
