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

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.