Fixed point results in controlled revised fuzzy metric spaces with an application to the transformation of solar energy to electric power

Abstract

Introduction/purpose: This study establishes sufficient conditions for a sequence to be Cauchy within the framework of controlled revised fuzzy metric spaces. It also generalizes the concept of Banach's contraction principle by introducing several new contraction conditions. The aim is to derive various fixed-point results that enhance the understanding of these mathematical structures. Methods: The researchers employ rigorous mathematical techniques to develop their findings. By defining a set of novel contraction mappings and utilizing properties of controlled revised fuzzy metric spaces, they analyze the implications for sequence convergence. The methodology includes constructing specific examples to illustrate the theoretical results. Results: The study presents several fixed-point theorems derived from the generalized contraction conditions. Additionally, it provides a number of non-trivial examples that substantiate the claims and demonstrate the applicability of the results in practical scenarios. A significant application is explored regarding the conversion of solar energy into electric power, utilizing differential equations to highlight this connection. Conclusion: The findings deepen the understanding of Cauchy sequences in fuzzy metric spaces and offer a broader perspective on the application of the fixed-point theory in real-world scenarios. The results pave the way for further research in both theoretical mathematics and its practical applications, particularly in the field of renewable energy.

Keywords

• fixed point theorems
• revised fuzzy metric space (rfms)
• contraction principles(cp)
• green’s function
• differential equation