Quasi Metric Space with Binary Operation and Fixed Point Theorems
DOI:
https://doi.org/10.62054/ijdm/0204.01Keywords:
Quasi-metric space, binary operation, fixed point theorem, contractive mapping, asymmetry.Abstract
This paper develops a novel framework termed quasi-metric space with binary operation, which extends the concept of a metric space with binary operation introduced by Adewale et al. (2025). While their construction was based on a symmetric metric structure, the present study relaxes this assumption and considers quasi-metrics that allow asymmetry in distances. This generalization enables the exploration of non-reciprocal systems and direction sensitive mappings. We introduce operational quasi-metric spaces, establish new structural properties, and derive several fixed point theorems for contractive-type mappings. Illustrative examples demonstrate the
validity and generality of the results. Applications to convergence analysis and stability in computational systems are also outlined. Our findings generalise many known results and extend the theory of metric-type fixed points into the asymmetric domain.
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Copyright (c) 2025 Ayodele S. Olusola, Adewale O. Kayode, Raji R.Adedoyin, Osawaru, E. Kelly, Iluno Christiana, Oyelade B. Eriwa (Author)
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