Inertial iterative method with self-adaptive step size for finite family of split monotone variational inclusion and fixed point problems in Banach spaces

• Autorzy: Ogwo Grace N. , Alakoya Timilehin O. , Mewomo Oluwatosin T.

Identyfikatory

DOI

10.1515/dema-2022-0005

• Języki publikacji: EN

Abstrakty

EN

In this paper, we propose and study a new inertial iterative algorithm with self-adaptive step size for approximating a common solution of finite family of split monotone variational inclusion problems and fixed point problem of a nonexpansive mapping between a Banach space and a Hilbert space. This method combines the inertial technique with viscosity method and self-adaptive step size for solving the common solution problem. We prove a strong convergence result for the proposed method under some mild conditions. Moreover, we apply our result to study the split feasibility problem and split minimization problem. Finally, we provide some numerical experiments to demonstrate the efficiency of our method in comparison with some well-known methods in the literature. Our method does not require prior knowledge or estimate of the operator norm, which makes it easily implementable unlike so many other methods in the literature, which require prior knowledge of the operator norm for their implementation.

Słowa kluczowe

EN

split monotone variational inclusion problem; split problem; nonexpansive mappings; Lipschitzian; fixed point problem; iterative schemes; split feasibility problem; split minimization problem

PL

zagadnienie równowagi; odwzorowania; problem punktu stałego; schemat iteracyjny; problem równowagi

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2022
• Tom: Vol. 55, nr 1
• Strony: 193--216
• Opis fizyczny: Bibliogr. 60 poz., tab., wykr.

Twórcy

autor

Ogwo Grace N.

• 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

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 MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).