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On the zero point problem of monotone operators in Hadamard spaces

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Abstract

In this paper, by using products of finitely many resolvents of monotone operators, we propose an iterative algorithm for finding a common zero of a finite family of monotone operators and a common fixed point of an infinitely countable family of nonexpansive mappings in Hadamard spaces. We derive the strong convergence of the proposed algorithm under appropriate conditions. A common fixed point of an infinitely countable family of quasi-nonexpansive mappings and a common zero of a finite family of monotone operators are also approximated in reflexive Hadamard spaces. In addition, we define a norm on X◇ := spanX∗ and give an application of this norm, where X is an Hadamard space with dual space X∗. A numerical example to solve a nonconvex optimization problem will be exhibited in an Hadamard space to support our main results.

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Authors and Affiliations

  1. Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran

    G. Zamani Eskandani & M. Raeisi

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  1. G. Zamani Eskandani
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Eskandani, G.Z., Raeisi, M. On the zero point problem of monotone operators in Hadamard spaces. Numer Algor 80, 1155–1179 (2019). https://doi.org/10.1007/s11075-018-0521-3

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