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

• Autorzy: Olona Musa A. , Alakoya Timilehin O. , Owolabi Abd-semii O.-E. , Mewomo Oluwatosin T.

Identyfikatory

DOI

10.1515/dema-2021-0006

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

inertial; split generalized equilibrium problems; self-adaptive; step size; nonexpansive multi-valued mapping; firmly nonexpansive mapping; fixed point problem

PL

zagadnienie równowagi; samoadaptacja; odwzorowania wielowartościowe; mapowanie; problem punktu stałego

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2021
• Tom: Vol. 54, nr 1
• Strony: 47--67
• Opis fizyczny: Bibliogr. 55 poz., rys., tab.

Twórcy

autor

Olona Musa A.

• School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa

autor

Alakoya Timilehin O.

• School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa

autor

Owolabi Abd-semii O.-E.

• School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa

autor

Mewomo Oluwatosin T.

• School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa

Bibliografia

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Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).