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Results on fixed points in b-metric space by altering distance functions
N Seshagiri Rao1, Ahmad Aloqaily2,3, Nabil Mlaiki2
1Department of Mathematics & Statistics, School of Applied Science & Humanities, Vignan's Foundation for Science, Technology & Research, Vadlamudi-522213, Guntur, Andhra Pradesh State, India.
Heliyon
|August 7, 2024
Summary
This study proves the existence and uniqueness of fixed points for self-mappings in ordered b-metric spaces using generalized contractive conditions. It also explores coincident and coupled fixed points for pairs of self-maps.
Area of Science:
- Fixed point theory
- Nonlinear analysis
- Metric space topology
Background:
- Investigates fixed point theorems in generalized metric spaces.
- Explores contractive mappings and their properties.
- Introduces the concept of ordered b-metric spaces.
Purpose of the Study:
- To establish the existence and uniqueness of fixed points for self-mappings.
- To analyze coincident and coupled fixed points for pairs of self-maps.
- To apply the findings to solve nonlinear quadratic integral equations.
Main Methods:
- Utilizes a novel -generalized contractive condition.
- Incorporates altering distance functions with rational terms.
- Employs techniques from fixed point theory in ordered spaces.
Main Results:
- Proves the existence and uniqueness of fixed points under the specified conditions.
- Demonstrates conditions for coincident and coupled fixed points.
- Provides illustrative numerical examples.
Conclusions:
- The established fixed point theorems are applicable in ordered b-metric spaces.
- The results extend existing literature on generalized contractions.
- The application to integral equations highlights the practical relevance of the theory.
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