Some Compatible and Weakly-Compatible Four Self-Mapping Results Approach to Nonlinear Integral Equations in Fuzzy Cone Metric Spaces

This paper is aimed at proving some unique common fixed point theorems by using the compatible and weakly-compatible four self-mappings in fuzzy cone metric (FCM) space. We prove the results under the generalized rational contraction conditions in FCM spaces with the help of one self-map are continuous. Furthermore, we prove some rational contraction results with the weaker condition of the self-mapping continuity. Ultimately, our theoretical work has been utilized to prove the existence solution of the two nonlinear integral equations. This is an illustrative application of how FCM spaces can be used in other integral type operators.

Automated summary

This paper aims to prove unique common fixed point theorems by studying compatible and weakly-compatible four self-mappings in fuzzy cone metric space. Results are proved under generalized rational contraction conditions and with the assistance of one continuous self-map. Additionally, rational contraction results are proved with weaker conditions of self-mapping continuity. Ultimately, the theoretical work is applied to prove the existence of solutions of two nonlinear integral equations, demonstrating the application of fuzzy cone metric spaces in other integral type operators.