Accelerated Tseng’s Method for Finding Common Solution of Fixed Point, Variational Inequality and Zeros Problems in Reflexive Banach Spaces
DOI:
https://doi.org/10.29020/nybg.ejpam.v19i1.6977Keywords:
Variational Inequality Problem, Inertial term, Bregman Distance, Tseng's Method, Strong Convergence, Reflexive Banach Space, Common Fixed PointAbstract
In this paper, we propose a novel accelerated extrapolation version of Tseng's algorithm with a self-adaptive step size for approximating a common solution to pseudomonotone variational inequality problems, zeros of maximal and Bregman inverse strongly monotone operators, and common fixed points of a finite family of Bregman demigeneralized mappings in a real reflexive Banach spaces. Using the Bregman distance technique, we establish a strong convergence result under mild assumptions, without requiring prior knowledge of the Lipschitz constant of the operator with application to a convex minimization problem (CMP). Our findings generalize and improve several results in the existing literature.
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Copyright (c) 2026 Ajio Jude, Godwin Ugwunnadi, Bashir Ali, Maggie Aphane
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