Approximation results for split equilibrium problems and fixed point problems of nonexpansive semigroup in Hilbert spaces

Abstract

Abstract In this paper, we study a modified extragradient method for computing a common solution to the split equilibrium problem and fixed point problem of a nonexpansive semigroup in real Hilbert spaces. The weak and strong convergence characteristics of the proposed algorithm are investigated by employing suitable control conditions in such a setting of spaces. As a consequence, we provide a simplified analysis of various existing results concerning the extragradient method in the current literature. We also provide a numerical example to strengthen the theoretical results and the applicability of the proposed algorithm.

Keywords

• Extragradient method
• Split equilibrium problem
• Fixed point problem
• Nonexpansive semigroup
• Weak and strong convergence