On the proximal point algorithm and demimetric mappings in CAT(0) spaces

• Autorzy: Aremu K. O. , Izuchukwu C. , Ugwunnadi G. C. , Mewomo O. T.

Identyfikatory

DOI

10.1515/dema-2018-0022

• Języki publikacji: EN

Abstrakty

EN

In this paper, we introduce and study the class of demimetric mappings in CAT(0) spaces. We then propose a modified proximal point algorithm for approximating a common solution of a finite family of minimization problems and fixed point problems in CAT(0) spaces. Furthermore, we establish strong convergence of the proposed algorithm to a common solution of a finite family of minimization problems and fixed point problems for a finite family of demimetric mappings in complete CAT(0) spaces. A numerical example which illustrates the applicability of our proposed algorithm is also given. Our results improve and extend some recent results in the literature.

Słowa kluczowe

EN

demimetric mappings; minimization problem; CAT(0) space; fixed point problem

PL

odwzorowania; problem minimalizacyjny; przestrzenie CAT(0); problem punktu stałego

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2018
• Tom: Vol. 51, nr 1
• Strony: 277--294
• Opis fizyczny: Bibliogr. 52 poz., wykr.

Twórcy

autor

Aremu K. O.

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

autor

Izuchukwu C.

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

autor

Ugwunnadi G. C.

• Department of Mathematics, University of Eswatini, Kwaluseni, Eswatini

autor

Mewomo O. T.

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

Bibliografia

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Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).