ON A DOUBLE INERTIAL MANN-TYPE METHOD FOR BREGMAN-DEMIGENERALIZED FIXED POINT AND VARIATIONAL INEQUALITY PROBLEMS

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.