Extended unique fixed point theorem in complete quasi-metric space
DOI:
https://doi.org/10.17721/1812-5409.2026/1.2Keywords:
fixed point, contraction mapping, complete metric space, complete quasi metric spaceAbstract
The primary goal of this research is to present novel fixed point theorems within the framework of complete quasi-metric spaces. Fixed point theory is a critical area connecting pure and applied mathematics. While classical results like the Banach contraction principle are well-established in metric spaces, this paper extends these concepts to the more generalized quasi-metric space, which lacks the symmetric condition of a standard metric space. We prove a unique fixed point theorem for continuous mappings in a complete quasi-metric space under a newly defined, comprehensive contractive condition. This result significantly generalizes and extends several existing fixed-point theorems in the literature. An example is provided to illustrate the applicability of our findings. Our work contributes to the development of fixed point theory in asymmetric spaces, which have applications in diverse fields such as shape-memory alloys and Hamilton - Jacobi equations.
Pages of the article in the issue: 13 - 16
Language of the article: English
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Copyright (c) 2026 Anurag Kumar, Aparna Vyas, Gibak Kim
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