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Regularization Methods and Iterative Methods for Variational Inequality with Accretive Operator
Nguyen Thi Thu Thuy

 

Abstract

We consider a regularization method based on the Browder–Tikhonov and iterative regularization method that can be used to find a solution of a class of accretive variational inequalities in a q-uniformly smooth Banach space, and the solutions are sought in the set of common fixed points of a countable family of nonexpansive mappings. We also introduce an iteration method, which is implicit and converges strongly, based on the steepest descent method with a strongly accretive and strictly pseudocontractive mapping. Our results generalize and extend some well-known regularization methods in the literature.