A strong convergence theorem for generalized-Φ-strongly monotone maps, with applications

Abstract Let X be a uniformly convex and uniformly smooth real Banach space with dual space X∗ $X^{*}$. In this paper, a Mann-type iterative algorithm that approximates the zero of a generalized-Φ-strongly monotone map is constructed. A strong convergence theorem for a sequence generated by the algo...

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Autores principales:	C. E. Chidume, M. O. Nnakwe, A. Adamu
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2019
Materias:	Generalized-Φ-strongly monotone map Optimization problem Hammerstein integral equation Variational inequality problem Strong convergence Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433
Acceso en línea:	https://doaj.org/article/9883bb84ed6a4efba6f8d7ad52d0c74d
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spelling	oai:doaj.org-article:9883bb84ed6a4efba6f8d7ad52d0c74d2021-12-02T12:10:25ZA strong convergence theorem for generalized-Φ-strongly monotone maps, with applications10.1186/s13663-019-0660-91687-1812https://doaj.org/article/9883bb84ed6a4efba6f8d7ad52d0c74d2019-06-01T00:00:00Zhttp://link.springer.com/article/10.1186/s13663-019-0660-9https://doaj.org/toc/1687-1812Abstract Let X be a uniformly convex and uniformly smooth real Banach space with dual space X∗ $X^{*}$. In this paper, a Mann-type iterative algorithm that approximates the zero of a generalized-Φ-strongly monotone map is constructed. A strong convergence theorem for a sequence generated by the algorithm is proved. Furthermore, the theorem is applied to approximate the solution of a convex optimization problem, a Hammerstein integral equation, and a variational inequality problem. This theorem generalizes, improves, and complements some recent results. Finally, examples of generalized-Φ-strongly monotone maps are constructed and numerical experiments which illustrate the convergence of the sequence generated by our algorithm are presented.C. E. ChidumeM. O. NnakweA. AdamuSpringerOpenarticleGeneralized-Φ-strongly monotone mapOptimization problemHammerstein integral equationVariational inequality problemStrong convergenceApplied mathematics. Quantitative methodsT57-57.97AnalysisQA299.6-433ENFixed Point Theory and Applications, Vol 2019, Iss 1, Pp 1-19 (2019)
institution	DOAJ
collection	DOAJ
language	EN
topic	Generalized-Φ-strongly monotone map Optimization problem Hammerstein integral equation Variational inequality problem Strong convergence Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433
spellingShingle	Generalized-Φ-strongly monotone map Optimization problem Hammerstein integral equation Variational inequality problem Strong convergence Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433 C. E. Chidume M. O. Nnakwe A. Adamu A strong convergence theorem for generalized-Φ-strongly monotone maps, with applications
description	Abstract Let X be a uniformly convex and uniformly smooth real Banach space with dual space X∗ $X^{*}$. In this paper, a Mann-type iterative algorithm that approximates the zero of a generalized-Φ-strongly monotone map is constructed. A strong convergence theorem for a sequence generated by the algorithm is proved. Furthermore, the theorem is applied to approximate the solution of a convex optimization problem, a Hammerstein integral equation, and a variational inequality problem. This theorem generalizes, improves, and complements some recent results. Finally, examples of generalized-Φ-strongly monotone maps are constructed and numerical experiments which illustrate the convergence of the sequence generated by our algorithm are presented.
format	article
author	C. E. Chidume M. O. Nnakwe A. Adamu
author_facet	C. E. Chidume M. O. Nnakwe A. Adamu
author_sort	C. E. Chidume
title	A strong convergence theorem for generalized-Φ-strongly monotone maps, with applications
title_short	A strong convergence theorem for generalized-Φ-strongly monotone maps, with applications
title_full	A strong convergence theorem for generalized-Φ-strongly monotone maps, with applications
title_fullStr	A strong convergence theorem for generalized-Φ-strongly monotone maps, with applications
title_full_unstemmed	A strong convergence theorem for generalized-Φ-strongly monotone maps, with applications
title_sort	strong convergence theorem for generalized-φ-strongly monotone maps, with applications
publisher	SpringerOpen
publishDate	2019
url	https://doaj.org/article/9883bb84ed6a4efba6f8d7ad52d0c74d
work_keys_str_mv	AT cechidume astrongconvergencetheoremforgeneralizedphstronglymonotonemapswithapplications AT monnakwe astrongconvergencetheoremforgeneralizedphstronglymonotonemapswithapplications AT aadamu astrongconvergencetheoremforgeneralizedphstronglymonotonemapswithapplications AT cechidume strongconvergencetheoremforgeneralizedphstronglymonotonemapswithapplications AT monnakwe strongconvergencetheoremforgeneralizedphstronglymonotonemapswithapplications AT aadamu strongconvergencetheoremforgeneralizedphstronglymonotonemapswithapplications
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A strong convergence theorem for generalized-Φ-strongly monotone maps, with applications

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