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Research Article Open access CC BY 4.0

Fixed Points of \(\xi\) - (\(\alpha\), \(\beta\))- Contractive Mappings in b-Metric Spaces

Kapil Jain, Jatinderdeep Kaur, Satvinder Singh Bhatia

Journal of Advances in Mathematics and Computer Science · pp. 6–15 · Published 22 Mar 2023

10.9734/jamcs/2023/v38i61764

Abstract

In the paper [Some new observations on Geraghty and \(\acute{C}\)iri\(\acute{c}\) type results in b-metric spaces, Mathematics, 7, (2019), doi: 10.3390/math7070643] Mlaiki et al. introduced (\(\alpha\), \(\beta\))-type contraction in order to generalize the contraction mapping defined by Pant and Panicker. Also, in the paper [Some fixed point results in b- metric spaces and b-metric-like spaces with new contractive mappings, Axioms, 10(2), (2021), 15 pages, doi: 10.3390/axioms10020055] Jain and Kaur presented the concepts of \(\xi\) -contractive mappings. Now, the aim of the present article is to introduce \(\xi\) - (\(\alpha\), \(\beta\)) -contractive mappings in b-metric spaces by combining the concepts (\(\alpha\), \(\beta\))-type contraction and \(\xi\)-contractive mappings. Also, we establish some fixed point results for newly defined mappings. Our results generalize various theorems in literature. In support, we provide an example.

b-metric space (\(\alpha\), \(\beta\))-admissible mappings (\(\alpha\), \(\beta\))-type contraction \(\xi\)-contractive mappings Cauchy Sequence fixed point

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