An Alternative Regularization Method for Equilibrium Problems and Fixed Point of Nonexpansive Mappings

The set of solutions of 1.1 is denoted by EP φ . Given a mapping T : C → H, let φ x, y 〈Tx, y − x〉 for all x, y ∈ C. Then, z ∈ EP φ if and only if 〈Tz, y − z〉 ≥ 0 for all y ∈ C, that is, z is a solution of the variational inequality. Numerous problems in physics, optimization, and economics reduce to find a solution of 1.1 . Some methods have been proposed to solve the equilibrium problem; see, for instance, 1–6 . A mapping S of C intoH is said to be nonexpansive if