A generalized Suzuki-Berinde contraction that characterizes Banach spaces

• Autorzy: Abbas Mujahid , Anjum Rizwan , Rakočević Vladimir

Identyfikatory

DOI

10.1515/jaa-2022-2007

• Języki publikacji: EN

Abstrakty

EN

We introduce a large class of contractive mappings, called Suzuki-Berinde type contraction. We show that any Suzuki-Berinde type contraction has a fixed point and characterizes the completeness of the underlying normed space. A fixed point theorem for multivalued mappings is also obtained. These results unify, generalize and complement various known comparable results in the literature.

Słowa kluczowe

EN

fixed point; completeness; Suzuki-Berinde type contraction; multivalued mapping

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2023
• Tom: Vol. 29, nr 2
• Strony: 239--250
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Abbas Mujahid

• Department of Mathematics, Government College University, Katchery Road, Lahore 54000, Pakistan
• Department of Mathematics and Applied Mathematics, University of Pretoria, Hatfield 002, Pretoria, South Africa

autor

Anjum Rizwan

• Abdus Salam School of Mathematical Sciences, Government College University, Lahore, Pakistan,

autor

Rakočević Vladimir

• Department of Mathematics, Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, Niš 18000, Serbia

Bibliografia

• [1] S. Banach, Sur les opérations dans les ensembles abstraits et leurs applications aux équations intégrales, Fund. Math. 3 (1922), 133-181.
• [2] I. Beg and S. M. A. Aleomraninejad, Fixed points of Suzuki type multifunctions on metric spaces, Rend. Circ. Mat. Palermo (2) 64 (2015), 203-207.
• [3] M. Edelstein, On fixed and periodic points under contractive mappings, J. Lond. Math. Soc. 37 (1962), 74-79.
• [4] M. Kikkawa and T. Suzuki, Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal. 69 (2008), no. 9, 2942-2949.
• [5] T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861-1869.
• [6] T. Suzuki, A new type of fixed point theorem in metric space, Nonlinear Anal. 71 (2009), 5313-5317.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).