On Rational Contractions of Geraghty-Fisher Type in Controlled Fuzzy Metric Spaces with Application

Dr. Shraddha Rajput

doi:10.5269/bspm.78958

Dr. Shraddha Rajput Shri Shankaracharya Professional University Bhilai C.G.

Abstract

This paper presents a novel rational contraction condition of the Geraghty-Fisher type within the framework of controlled fuzzy metric spaces, thereby extending and strengthening existing fixed point results. The proposed contraction condition provides a more general and effective approach for establishing fixed points in fuzzy environments. To validate the theoretical findings, an illustrative example is included along with a graphical representation demonstrating convergence. Moreover, the applicability of the theorem is illustrated by proving the existence and uniqueness of solutions for a second-order differential equation associated with a two-point boundary value problem in electric circuit theory. The results obtained not only generalize several known fixed point theorems but also offer new mathematical tools applicable to real-world problems in engineering and applied sciences. This work contributes to the advancement of fixed point theory and opens avenues for further research in fuzzy metric spaces and their applications.

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