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Fixed point results for ℑ-Contractions in JS-generalized metric spaces with an application
Bilal Iqbal1, Naeem Saleem1,2, Maggie Aphane2
1Department of Mathematics, University of Management and Technology, Lahore, Pakistan.
Plos One
|February 18, 2025
Summary
This study introduces ℑ-contractions and proves new fixed-point theorems in generalized metric spaces. These findings are then applied to demonstrate the existence of solutions for RLC circuit differential equations.
Area of Science:
- Mathematics
- Nonlinear Analysis
- Metric Space Theory
Background:
- Fixed-point theory is crucial for solving equations.
- Generalized metric spaces offer a broader framework for analysis.
- RLC circuits are fundamental in electrical engineering.
Purpose of the Study:
- To introduce and define ℑ-contractions.
- To establish novel fixed-point theorems for ℑ-contractions.
- To apply these theorems to solve RLC circuit differential equations.
Main Methods:
- Development of ℑ-contraction mappings.
- Application of fixed-point theorems in generalized metric spaces.
- Analysis of differential equations using fixed-point results.
Main Results:
- The existence and properties of ℑ-contractions are established.
- New fixed-point theorems are proven for these contractions.
- An existence result for the RLC circuit's current differential equation is demonstrated.
Conclusions:
- ℑ-contractions provide a new tool in fixed-point theory.
- The study expands the applicability of fixed-point theorems.
- The research offers a theoretical basis for analyzing RLC circuit behavior.
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