ON SELECTION ALGORITHM

Abstract

COMMUNICATION IN PHYSICAL SCIENCES 3(1):1-9

Received 14 November 2017/Accepted 13 July 2018

Author: F.O. Isiogugu

Strong convergence of an iteration scheme for approximating the common elements of the set of solutions EP(F) of an equilibrium problem for a bifunction F and the set of fixed points F(T) of a multi-valued(or single-valued) hemicontractive mapping T is established in a real Hilbert space H. This work contributes to the study on the applicability and computability of iteration schemes for bifunctions involving the construction of the sequence{K_n}^∞_n=1 of closed convex subsets of H from an arbitrary x_o ∈ H and the sequence {x_n}^∞_n=1 of the metric projections of x_o into K_n. The results obtained extend and improve many results in this direction in the contemporary literature.