An extragradient inertial algorithm for solving split fixed-point problems of demicontractive mappings, with equilibrium and variational inequality problems

• Autorzy: Okeke Chibueze C. , Ugwunnadi Godwin C. , Jolaoso Lateef O.

Identyfikatory

DOI

10.1515/dema-2020-0120

• Języki publikacji: EN

Abstrakty

EN

The purpose of this article is to study and analyse a new extragradient-type algorithm with an inertial extrapolation step for solving split fixed-point problems for demicontractive mapping, equilibrium problem, and pseudomonotone variational inequality problem in real Hilbert spaces. One of the advantages of the proposed algorithm is that a strong convergence result is achieved without a prior estimate of the Lipschitz constant of the cost operator, which is very difficult to find. In addition, the stepsize is generated at each iteration by some simple computations, which allows it to be easily implemented without the prior knowledge of the Lipschitz constant of the cost operator. Some numerical experiments are reported to show the performance and behaviour of the sequence generated by our algorithm. The obtained results in this article extend and improve many related recent results in this direction in the literature.

Słowa kluczowe

EN

variational inequality problem; pseudo-monotone operator; viscosity iteration; equilibrium problem; demicontractive mappings; split fixed point; Hilbert space

PL

nierówność wariacyjna; operator pseudo-monotoniczny; iteracja; zagadnienie równowagi; punkt stały; przestrzeń Hilberta

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2022
• Tom: Vol. 55, nr 1
• Strony: 506--527
• Opis fizyczny: Bibliogr. 37 poz., tab., wykr.

Twórcy

autor

Okeke Chibueze C.

• School of Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South Africa

autor

Ugwunnadi Godwin C.

• Department of Mathematics, University of Eswatini, Private Bag 4, Kwaluseni, Eswatini
• Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, P.O. Box 94 Medunsa 0204, Pretoria, South Africa

autor

Jolaoso Lateef O.

• Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, P.O. Box 94 Medunsa 0204, Pretoria, South Africa
• Federal University of Agriculture, Abeokuta, Nigeria

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).