A STEEPEST-DESCENT KRASNOSEL’SKII–MANN ALGORITHM FOR AN INFINITE FAMILY OF NONEXPANSIVE MAPPINGS

Nguyen Thi Thu Thuy

Abstract


For solving a variational inequality problem over the common fixed point set of an infinite family of nonexpansive mappings on uniformly smooth Banach spaces or reflexive and strictly convex ones with a uniformly Gâteaux differentiable norm, we consider an explicit iteration method, based on the steepest-descent and Krasnosel’skii–Mann algorithms. We also show that some modifications of the last are special case of our result.


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ISSN: 1229-1595 (Print), 2466-0973 (Online)

(51767) 7 Kyungnamdaehak-ro, Masanhappo-gu, Changwon-si, Gyeongsangnam-do, Republic of Korea