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In this paper, we mainly introduce a new and different self adaptive extragradient algorithm with an inertial technique for solving variational inequality problems of pseudomonotone operators and fixed point problems of relatively nonexpansive mappings in 2-uniformly convex and uniformly smooth Banach spaces. Under some appropriate assumptions imposed on the parameters and operators, we prove that the iterative sequence generated by our proposed algorithm converges strongly to a common solution of variational inequality problems and fixed point problems. Moreover, we give some numerical examples to show the effectiveness and feasibility of our algorithm.

numerical functional analysis and optimization

Self-Adaptive Extragradient Methods for Solving Variational Inequalities and Fixed Point Problems in 2-Uniformly Convex and Uniformly Smooth Banach Spaces