@article{Alharbi2025, 
author = {Mohammed H. Alharbi and Jamshaid Ahmad},
title = {A fresh look at Volterra integral equations: a fixed point approach in        F  -bipolar metric spaces},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {4},
pages = {8926-8945},
keywords = {fixed point, F-bipolar metric space, rational contraction, Volterra integral equation, homotopy theory},
url = {https://www.sciopen.com/article/10.3934/math.2025409},
doi = {10.3934/math.2025409},
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        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.}
}