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Unique fixed point theorems in partially ordered metric spaces
1Department of Applied Mathematics, School of Applied Natural Sciences, Adama Science and Technology University, Post Box No. 1888, Adama, Ethiopia.
Heliyon
|December 9, 2020
Summary
This study establishes fixed point theorems for rational contractive mappings in partially ordered metric spaces. These findings generalize existing results, offering new insights into fixed point theory.
Area of Science:
- Mathematics
- Fixed Point Theory
- Metric Spaces
Background:
- Fixed point theory is crucial in various mathematical fields.
- Partially ordered metric spaces provide a rich framework for studying mappings.
- Previous research has explored contractive conditions in these spaces.
Purpose of the Study:
- To establish new fixed point results for rational type contractive mappings.
- To generalize and extend existing theorems in partially ordered metric spaces.
- To contribute to the advancement of fixed point theory.
Main Methods:
- Utilizing rational type contractive conditions.
- Working within the framework of metric spaces endowed with partial order.
- Applying techniques from fixed point theory.
Main Results:
- New fixed point theorems are established for the specified mappings.
- The results generalize and extend prior work, including Singh and Chatterjee (1988).
- Illustrative examples are provided to validate the theoretical findings.
Conclusions:
- The established fixed point results are significant extensions in the field.
- The study enhances understanding of contractive mappings in partially ordered metric spaces.
- The findings have implications for further research in fixed point theory.
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