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Boyd-Wong type contractions in generalized parametric bipolar metric space
Manoj Kumar1, Ozgur Ege2, Vinit Mor1
1Department of Mathematics, Baba Mastnath University, Asthal Bohar, Rohtak, 124021, Haryana, India.
Heliyon
|January 25, 2024
Summary
This study introduces generalized parametric bipolar metric spaces and Boyd-Wong type contractions to establish fixed-point theorems. These findings are applied to solve integral and fractional differential equations.
Area of Science:
- Mathematics
- Analysis
- Topology
Background:
- Existing research in generalized parametric spaces and bipolar metric spaces.
- The need for a unified framework to study fixed-point theorems.
Purpose of the Study:
- To introduce and define a new mathematical space: generalized parametric bipolar metric space.
- To extend the theory of contractions and fixed-point results to this new space.
- To demonstrate the applicability of the new results in solving differential equations.
Main Methods:
- Definition of generalized parametric bipolar metric spaces.
- Introduction of Boyd-Wong type contractions for covariant and contravariant mappings.
- Application of fixed-point theorems to integral and fractional differential equations.
Main Results:
- Establishment of fixed-point theorems in the newly defined generalized parametric bipolar metric space.
- Illustration of results with examples and corollaries for Banach type contractions.
- Demonstration of the utility of the theorems in solving integral and fractional differential equations.
Conclusions:
- The proposed generalized parametric bipolar metric space offers a broader framework for fixed-point theory.
- The developed fixed-point theorems have practical applications in solving complex equations.
- This work contributes to the advancement of metric space theory and its applications.
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