Acta Mathematica Vietnamica

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A strongly convergent shrinking descent-like Halpern's method for monotone variational inequality and fixed point problems
Nguyen Thi Thu Thuy

 

Abstract

In this paper, we introduce a new iteration method based on the hybrid method in mathematical programming, the descent-like method and the Halpern’s iteration method for finding a common element of the solution set for a variational inequality and the set of common fixed points of a countably infinite family of nonexpansive mappings in Hilbert spaces. The result in this paper modifies and improves some well-known results in the literature for a more general problem.

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