A Modified Inertial Ishikawa and $CQ$ Algorithm for Equilibrium Problems and Generalized $2$-Hybrid Mappings

Alizadeh, Sattar; Moradlou, Fridoun

doi:10.22055/jamm.2026.51221.2449

A Modified Inertial Ishikawa and $CQ$ Algorithm for Equilibrium Problems and Generalized $2$-Hybrid Mappings

Articles in Press

Document Type : Original Paper

Authors

Sattar Alizadeh ¹

fridoun Moradlou ²

¹ Department of Mathematics, Marand Branch, Islamic Azad University, Marand, Iran

² ‎Department of Mathematics‎‎, ‎Sahand University of Technology‎, ‎Tabriz‎, ‎Iran‎

10.22055/jamm.2026.51221.2449

Abstract

‎In this paper‎, ‎we introduce a novel hybrid algorithm for finding a common element between the solution set of an equilibrium problem and the fixed point set of nonlinear mappings in a Hilbert space‎. ‎The bifunctions used satisfy standard conditions of monotonicity and continuity‎, ‎and the mapping under consideration is a $2$-generalized hybrid mapping that encompasses a wide class of nonlinear mappings‎, ‎including nonexpansive‎, ‎nonspreading‎, ‎and hybrid mappings‎. ‎Using the proposed algorithm‎, ‎we establish a strong convergence theorem‎. ‎Two numerical examples are presented along with a convergence table and comparative tables‎, ‎demonstrating the efficiency of the algorithm in terms of simplicity and convergence speed compared to classical methods‎. ‎The numerical results highlight the structural simplicity and superior convergence rate of the proposed algorithm over traditional iterative schemes‎.

Keywords

Inertial algorithm

Fixed point

Hilbert space

strong convergence

Subjects