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On combinational contractions with applications.
Mohammed Shehu Shagari1, Manzuma Mustapha1, Hala H Taha2
1Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria.
Heliyon
|February 5, 2025
Summary
This study introduces a novel hybrid contraction, combining Jaggi, Meir-Keeler, and Zamfirescu types, to prove fixed-point theorems in complete metric spaces. The findings offer new methods for solving nonlinear Fredholm integral equations.
Area of Science:
- Mathematical Analysis
- Fixed-Point Theory
Background:
- Metric spaces are fundamental in analysis.
- Fixed-point theory seeks solutions to equations.
- Existing contraction types have limitations.
Purpose of the Study:
- To introduce a new hybrid contraction combining Jaggi, Meir-Keeler, and Zamfirescu types.
- To investigate the existence and uniqueness of fixed points for this new contraction.
- To apply the new contraction to solve nonlinear Fredholm integral equations.
Main Methods:
- Developing a novel hybrid contraction.
- Utilizing the framework of complete metric spaces.
- Proving existence and uniqueness theorems for fixed points.
Main Results:
- A new hybrid contraction is successfully formulated.
- Conditions for the existence and uniqueness of fixed points are established.
- A validating example demonstrates the results' efficacy.
Conclusions:
- The new hybrid contraction provides a powerful tool in fixed-point theory.
- The research offers novel criteria for solving nonlinear Fredholm integral equations.
- This work expands the applicability of fixed-point theorems.
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