A Halpern-Mann Type Iteration for Fixed Point Problems of a Relatively Nonexpansive Mapping and a System of Equilibrium Problems

الملخص EN

A new modified Halpern-Mann type iterative method is constructed.

Strong convergence of the scheme to a common element of the set of fixed points of a relatively nonexpansive mapping and the set of common solutions to a system of equilibrium problems in a uniformly convex real Banach space which is also uniformly smooth is proved.

The results presented in this work improve on the corresponding ones announced by many others.