Optimization Eruditorum

Electronic ISSN: 3008-1521

DOI: 10.69829/oper

An inertial iterative method for generalized mixed equilibrium problem and fixed point problem of nonexpansive semigroups

Optimization Eruditorum, Volume 2, Issue 2, August 2025, Pages 116–131

ABDELLAH BNOUHACHEM

Equipe MAISI, Ibn Zohr University, ENSA, BP 1136, Agadir, Morocco


Abstract

To approximate common solutions for generalized mixed equilibrium problems involving monotone and uniformly continuous operators and fixed point problem of nonexpansive semigroups in real Hilbert spaces, we introduce an inertial extragradient algorithm with non-monotone step sizes. This algorithm, derived from a combination of extragradient and viscosity methods, ensures strong convergence without needing to estimate the operator's Lipschitz constant. The algorithm's effectiveness is supported by a numerical example, showcasing its efficiency.


Cite this Article as

Abdellah Bnouhachem, An inertial iterative method for generalized mixed equilibrium problem and fixed point problem of nonexpansive semigroups, Optimization Eruditorum, 2(2), 116–131, 2025