Mann iteration for monotone nonexpansive mappings in ordered CAT(0) space with an application to integral equations

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URI: http://hdl.handle.net/10347/19952
E-ISSN: 1029-242X
DOI: 10.1186/s13660-018-1925-2

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2018-12-11

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Abstract

In this paper, we establish some convergence results for a monotone nonexpansive mapping in a CAT(0) space. We prove the Δ- and strong convergence of the Mann iteration scheme. Further, we provide a numerical example to illustrate the convergence of our iteration scheme, and also, as an application, we discuss the solution of integral equation. Our results extend some of the relevant results

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CAT(0) space| Fixed point| Δ-convergence| Monotone nonexpansive mapping

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Uddin, I., Garodia, C., & Nieto, J. (2018). Mann iteration for monotone nonexpansive mappings in ordered CAT(0) space with an application to integral equations. Journal Of Inequalities And Applications, 2018(1). doi: 10.1186/s13660-018-1925-2

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The first author is thankful to University Grants Commission, India for the financial assistance in form of BSR-Startupreserach grant. The second author is grateful to University Grants Commission, India, for providing financial assistance in the form of the Junior Research Fellowship. The research of J.J. Nieto has been partially supported by AEI of the Ministerio de Economia y Competitividad of Spain under Grant MTM2016-75140-P and cofinanced by European Community fund FEDER and XUNTA de Galicia under grants GRC2015-004 and R2016/022

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© The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made

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Estatística, Análise Matemática e Optimización