A SPECTRAL GRADIENT PROJECTION METHOD FOR
ZEROS OF MULTI-VALUED MONOTONE FUNCTIONS
IN HILBERT SPACES
Ma'aruf S. Minjibir1, Musa Ilyasu1
1 Bayero University, Kano
Department of Mathematical Sciences
Kabuga/Gwarzo Road
Kano - 700341, NIGERIA

Abstract

An algorithm for zeros of single-valued monotone maps in the setting of the finite dimensional Hilbert spaces $\mathbb{R}^{n} $ is considered in the more general setting of infinite dimensional Hilbert spaces. The sequence generated from the algorithm is shown to globally converge weakly to a solution of a zero problem in any infinite dimensional real Hilbert space. For the more general multi-valued case, a modified version of the algorithm is presented and the sequence generated is shown to globally converge weakly to a solution of the multi-valued zero problem. Moreover, the algorithm does not involve computing resolvent of the monotone map.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 36
Issue: 1
Year: 2023

DOI: 10.12732/ijam.v36i1.4

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