Journals Information
Mathematics and Statistics Vol. 13(5), pp. 320 - 328
DOI: 10.13189/ms.2025.130507
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A Fixed Point Theorem on Metric-like Spaces of Hyperbolic Type
Silvja 脟obani 1,*, Elida Hoxha 2
1 Department of Mathematics and Physics, "Fan S. Noli" University, Kor莽毛, 7001 Kor莽毛, Albania
2 Department of Mathematics, University of Tirana, 1016 Tirana, Albania
ABSTRACT
The metric-like space was first introduced by Hitzler in 2000 as a generalization of the metric space which allows for non-zero self-distances. Since then, these spaces have become a focal point of research with regard not only to the investigation of fixed points of contractive mappings, but also to introducing new generalizations of this type of spaces. In this paper, we introduce and investigate a new type of metric-like spaces, referred to as metric-like spaces of hyperbolic type, a generalization of metrically convex metriclike spaces. This space maintains the dislocated properties of the metric-like space while satisfying a hyperbolic convexity criteria inspired by Kirk's 1972 formulation. Motivated by the foundational work of Banach and its subsequent extensions to the metric-like space, we establish a new fixed point result that expand the applicability of weak contractive conditions in the metric-like spaces of hyperbolic type. More precisely, we derive a fixed point theorem for multivalued mappings satisfying a generalized 
weak-type contractive condition. Our findings demonstrate that significant results in the literature can also be extended to the metric-like spaces of hyperbolic type. Moreover, an illustrative example is provided in the end to demonstrate the validity of the proposed theorem. This work contributes to the growing body of fixed point theory by extending and generalizing several existing results in the literature.
KEYWORDS
Metric-like Space, Multivalued Mapping, Fixed Point, Weak-type Contraction
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Silvja 脟obani , Elida Hoxha , "A Fixed Point Theorem on Metric-like Spaces of Hyperbolic Type," Mathematics and Statistics, Vol. 13, No. 5, pp. 320 - 328, 2025. DOI: 10.13189/ms.2025.130507.
(b). APA Format:
Silvja 脟obani , Elida Hoxha (2025). A Fixed Point Theorem on Metric-like Spaces of Hyperbolic Type. Mathematics and Statistics, 13(5), 320 - 328. DOI: 10.13189/ms.2025.130507.