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Open AccessArticle

Admissible Hybrid Z-Contractions in b-Metric Spaces

1
Department of Business, Babeş-Bolyai University Cluj-Napoca, Horea Street, No.7, 400000 Cluj-Napoca, Romania
2
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
*
Author to whom correspondence should be addressed.
Received: 25 November 2019 / Revised: 17 December 2019 / Accepted: 19 December 2019 / Published: 21 December 2019
(This article belongs to the Special Issue Nonlinear Analysis and Optimization with Applications)
In this manuscript, we introduce a new notion, admissible hybrid Z -contraction that unifies several nonlinear and linear contractions in the set-up of a b-metric space. In our main theorem, we discuss the existence and uniqueness result of such mappings in the context of complete b-metric space. The given result not only unifies the several existing results in the literature, but also extends and improves them. We express some consequences of our main theorem by using variant examples of simulation functions. As applications, the well-posedness and the Ulam–Hyers stability of the fixed point problem are also studied. View Full-Text
Keywords: admissible spaces; hybrid contraction; interpolative contraction; b-metric spaces; simulation function; interpolative contraction admissible spaces; hybrid contraction; interpolative contraction; b-metric spaces; simulation function; interpolative contraction
MDPI and ACS Style

Chifu, I.C.; Karapınar, E. Admissible Hybrid Z-Contractions in b-Metric Spaces . Axioms 2020, 9, 2.

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