On a Double Inertial Mann-type Method for Bregman-Demigeneralized Fixed Point and Variational Inequality Problems
Applicable Nonlinear Analysis, Volume 3, Issue 3, December 2026, Pages: 195–209
Godwin Ikechukwu Ezugorie
Department of Mathematics, Enugu State University of Science and Technology, Enugu, Nigeria
Abstract
In this paper, we introduce a new double inertial Mann-type iterative algorithm for approximating a common solution of a demigeneralized fixed point problem and a monotone variational inequality problem in reflexive Banach spaces. Our method is developed in the framework of Bregman distances generated by a Legendre function, which provides a more general geometric structure than the classical norm framework. Under suitable assumptions on the control parameters, the demigeneralized mapping, and the monotone operator, we establish strong convergence of the proposed algorithm to a common solution of the two problems. The results presented here extend and unify several existing schemes in the literature, including classical Halpern iterations, inertial methods, and Bregman projection-type approaches.
Cite this Article as
Godwin Ikechukwu Ezugorie, On a Double Inertial Mann-type Method for Bregman-Demigeneralized Fixed Point and Variational Inequality Problems, Applicable Nonlinear Analysis, 3(3), 195–209, 2026