A fresh look at Volterra integral equations: a fixed point approach in $ \mathfrak{F} $-bipolar metric spaces
Year: 2025
Type: article
Abstract: Our aim of the research article was to obtain fixed point results for generalized contractions equipped with precisely defined control functions in the framework of $ \mathfrak{F} $-bipolar metric spaces. As a consequence, some well-known results from the literature were derived as special cases of our leading theorems. To validate the theoretical findings and demonstrate their practical relevance, a non-trivial illustrative example is included. Furthermore, we explored the applicability of our major results by addressing the existence and uniqueness of solutions to Volterra integral equations, a class of problems frequently arising in mathematical modeling of real-world systems. In addition, we extended the utility of our fixed point theorems to homotopy theory, where they served as a foundational tool in analyzing the existence of continuous deformations between mappings, thereby contributing to the study of topological invariants and the structural properties of function spaces.
Source: AIMS Mathematics
DOI: 10.3934/math.2025409
Authors: Mohammed H. Alharbi, Jamshaid Ahmad
Institution: University of Jeddah
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,200
OpenAlex ID: W4409568582