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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio

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Mann iteration process for monotone nonexpansive mappings with a graph

Monther Rashed AlfuraidanORCID iD: http://orcid.org/0000-0002-3641-290X
Published Online: 2018-06-13 | DOI: https://doi.org/10.1515/gmj-2018-0036


Let (X,) be a Banach space. Let C be a nonempty, bounded, closed and convex subset of X and let T:CC be a G-monotone nonexpansive mapping. In this work, it is shown that the Mann iteration sequence defined by


proves the existence of a fixed point of G-monotone nonexpansive mappings.

Keywords: Directed graph; fixed point; Mann iteration process; monotone mapping; nonexpansive mapping; Opial condition; uniformly convex Banach space; weakly connected graph

MSC 2010: 06F30; 46B20; 47E10


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About the article

Received: 2015-07-15

Revised: 2016-04-15

Accepted: 2016-05-30

Published Online: 2018-06-13

Funding Source: King Fahd University of Petroleum and Minerals

Award identifier / Grant number: IP142-MATH-111

The author would like to acknowledge the support provided by the Deanship of Scientific Research at King Fahd University of Petroleum & Minerals for funding this work through project no. IP142-MATH-111.

Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2018-0036.

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