Abstract
By using a specific way of choosing the indexes, we propose an iteration algorithm generated by the monotone CQ method for approximating common fixed points of an infinite family of relatively quasinonexpansive mappings. A strong convergence theorem without the stronger assumptions of the AKTT condition and the ∗AKTT condition imposed on the involved mappings is established in the framework of Banach space. As application, an iterative solution to a system of equilibrium problems is studied. The result is more applicable than those of other authors with related interest.
Highlights
Let C be a nonempty and closed convex subset of a real Banach space E
Inspired and motivated by those studies mentioned above, in this paper, we use a modified type of the iteration scheme 1.8 for approximating common fixed points of an infinite family of relatively quasi-nonexpansive mappings; without stronger assumptions imposed on the involved mappings, a strong convergence theorem in Banach spaces is obtained for solving a system of equilibrium problems
We say that E is strictly convex if the following implication holds for x, y ∈ E: x y 1, x/y ⇒
Summary
Let C be a nonempty and closed convex subset of a real Banach space E. Inspired and motivated by those studies mentioned above, in this paper, we use a modified type of the iteration scheme 1.8 for approximating common fixed points of an infinite family of relatively quasi-nonexpansive mappings; without stronger assumptions imposed on the involved mappings, a strong convergence theorem in Banach spaces is obtained for solving a system of equilibrium problems. The results improve those of other authors with related interest
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 call
