Inertial shrinking projection algorithm with self-adaptive step size for split generalized equilibrium and fixed point problems for a countable family of nonexpansive multivalued mappings

In this paper, we introduce a shrinking projection method of an inertial type with self-adaptive step size for finding a common element of the set of solutions of a split generalized equilibrium problem and the set of common fixed points of a countable family of nonexpansive multivalued mappings in...

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Autores principales:	Olona Musa A., Alakoya Timilehin O., Owolabi Abd-semii O.-E., Mewomo Oluwatosin T.
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	inertial split generalized equilibrium problems self-adaptive step size nonexpansive multivalued mappings firmly nonexpansive mapping fixed point problems 65k15 47j25 65j15 90c33 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/d3a12060b91b4cc8986ba4d4e9d5b48e
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spelling	oai:doaj.org-article:d3a12060b91b4cc8986ba4d4e9d5b48e2021-12-05T14:10:45ZInertial shrinking projection algorithm with self-adaptive step size for split generalized equilibrium and fixed point problems for a countable family of nonexpansive multivalued mappings2391-466110.1515/dema-2021-0006https://doaj.org/article/d3a12060b91b4cc8986ba4d4e9d5b48e2021-04-01T00:00:00Zhttps://doi.org/10.1515/dema-2021-0006https://doaj.org/toc/2391-4661In this paper, we introduce a shrinking projection method of an inertial type with self-adaptive step size for finding a common element of the set of solutions of a split generalized equilibrium problem and the set of common fixed points of a countable family of nonexpansive multivalued mappings in real Hilbert spaces. The self-adaptive step size incorporated helps to overcome the difficulty of having to compute the operator norm, while the inertial term accelerates the rate of convergence of the proposed algorithm. Under standard and mild conditions, we prove a strong convergence theorem for the problems under consideration and obtain some consequent results. Finally, we apply our result to solve split mixed variational inequality and split minimization problems, and we present numerical examples to illustrate the efficiency of our algorithm in comparison with other existing algorithms. Our results complement and generalize several other results in this direction in the current literature.Olona Musa A.Alakoya Timilehin O.Owolabi Abd-semii O.-E.Mewomo Oluwatosin T.De Gruyterarticleinertialsplit generalized equilibrium problemsself-adaptivestep sizenonexpansive multivalued mappingsfirmly nonexpansive mappingfixed point problems65k1547j2565j1590c33MathematicsQA1-939ENDemonstratio Mathematica, Vol 54, Iss 1, Pp 47-67 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	inertial split generalized equilibrium problems self-adaptive step size nonexpansive multivalued mappings firmly nonexpansive mapping fixed point problems 65k15 47j25 65j15 90c33 Mathematics QA1-939
spellingShingle	inertial split generalized equilibrium problems self-adaptive step size nonexpansive multivalued mappings firmly nonexpansive mapping fixed point problems 65k15 47j25 65j15 90c33 Mathematics QA1-939 Olona Musa A. Alakoya Timilehin O. Owolabi Abd-semii O.-E. Mewomo Oluwatosin T. Inertial shrinking projection algorithm with self-adaptive step size for split generalized equilibrium and fixed point problems for a countable family of nonexpansive multivalued mappings
description	In this paper, we introduce a shrinking projection method of an inertial type with self-adaptive step size for finding a common element of the set of solutions of a split generalized equilibrium problem and the set of common fixed points of a countable family of nonexpansive multivalued mappings in real Hilbert spaces. The self-adaptive step size incorporated helps to overcome the difficulty of having to compute the operator norm, while the inertial term accelerates the rate of convergence of the proposed algorithm. Under standard and mild conditions, we prove a strong convergence theorem for the problems under consideration and obtain some consequent results. Finally, we apply our result to solve split mixed variational inequality and split minimization problems, and we present numerical examples to illustrate the efficiency of our algorithm in comparison with other existing algorithms. Our results complement and generalize several other results in this direction in the current literature.
format	article
author	Olona Musa A. Alakoya Timilehin O. Owolabi Abd-semii O.-E. Mewomo Oluwatosin T.
author_facet	Olona Musa A. Alakoya Timilehin O. Owolabi Abd-semii O.-E. Mewomo Oluwatosin T.
author_sort	Olona Musa A.
title	Inertial shrinking projection algorithm with self-adaptive step size for split generalized equilibrium and fixed point problems for a countable family of nonexpansive multivalued mappings
title_short	Inertial shrinking projection algorithm with self-adaptive step size for split generalized equilibrium and fixed point problems for a countable family of nonexpansive multivalued mappings
title_full	Inertial shrinking projection algorithm with self-adaptive step size for split generalized equilibrium and fixed point problems for a countable family of nonexpansive multivalued mappings
title_fullStr	Inertial shrinking projection algorithm with self-adaptive step size for split generalized equilibrium and fixed point problems for a countable family of nonexpansive multivalued mappings
title_full_unstemmed	Inertial shrinking projection algorithm with self-adaptive step size for split generalized equilibrium and fixed point problems for a countable family of nonexpansive multivalued mappings
title_sort	inertial shrinking projection algorithm with self-adaptive step size for split generalized equilibrium and fixed point problems for a countable family of nonexpansive multivalued mappings
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/d3a12060b91b4cc8986ba4d4e9d5b48e
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Inertial shrinking projection algorithm with self-adaptive step size for split generalized equilibrium and fixed point problems for a countable family of nonexpansive multivalued mappings

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