A different approach to b(αn,βn)-hypermetric spaces

DOI: https://doi.org/10.5937/vojtehg70-35303
Keywords: b(αn, βn) hypermetric spaces, G-metric, fixed-point

Abstract


Introduction/purpose: The aim of this paper is to present the concept of b(αn,βn)-hypermetric spaces.
Methods: Conventional theoretical methods of functional analysis.
Results: This study presents the initial results on the topic of b(αn,βn)-hypermetric spaces. In the first part, we generalize an n-dimensional (n ≥ 2) hypermetric distance over an arbitrary non-empty set X. The b(αn,βn)-hyperdistance function is defined in any way we like, the only constraint being the simultaneous satisfaction of the three properties, viz, non-negativity and positive-definiteness, symmetry and (αn, βn)-triangle inequality. In the second part, we discuss the concept of (αn, βn)-completeness, with respect to this b(αn,βn)-hypermetric, and the fixed point theorem which plays an important role in applied mathematics in a variety of fields.
Conclusion: With proper generalisations, it is possible to formulate well-known results of classical metric spaces to the case of b(αn,βn)-hypermetric spaces.

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Published
2022/01/05
Issue
Vol. 70 No. 1 (2022): January-March
Section
Original Scientific Papers
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