On Bregman Asymptotically Quasi-Nonexpansive Mappings and Generalized Variational-like Systems

Ghada AlNemer, Rehan Ali () and Mohammad Farid ()
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Ghada AlNemer: Department of Mathematical Sciences, College of Sciences, Princess Nourah bint Abdulrahman University, Riyadh 11671, Saudi Arabia
Rehan Ali: Department of Mathematics, Central University of Kashmir, Ganderbal 191131, Jammu and Kashmir, India
Mohammad Farid: Department of Mathematics, College of Science, Qassim University, Saudi Arabia

Mathematics, 2025, vol. 13, issue 22, 1-31

Abstract: In this work, we propose and study an inertial hybrid projection algorithm to approximate a common solution of a system of unrelated generalized mixed variational-like inequalities and the common fixed points of Bregman asymptotically quasi-nonexpansive mappings in the intermediate sense. We establish a strong convergence theorem for the generated sequence and derive several corollaries. Further, we provide applications of Bregman asymptotically quasi-nonexpansive mappings in the intermediate sense. Numerical examples are provided to demonstrate the effectiveness of the method, and we also present a comparative analysis.

Keywords: GMVLIP; FPP; Bregman distance; iterative methods; BAQNE; inertial method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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