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Fixed point results for weak contractions in partially ordered b-metric space
N Seshagiri Rao1, K Kalyani2, K Prasad3
1Department of Applied Mathematics, School of Applied Natural Sciences, Adama Science and Technology University, Post Box No.1888, Adama, Ethiopia. seshu.namana@gmail.com.
BMC Research Notes
|July 9, 2021
Summary
This study proves the existence and uniqueness of fixed points for mappings in ordered b-metric spaces using generalized weak contractions. It also establishes results for coincidence and coupled coincidence points for two mappings.
Area of Science:
- Mathematical Analysis
- Topology
Background:
- Ordered b-metric spaces provide a generalized framework for metric spaces.
- Fixed point theory is crucial for solving equations and understanding dynamical systems.
Purpose of the Study:
- To investigate the existence and uniqueness of fixed points for mappings in ordered b-metric spaces.
- To explore coincidence and coupled coincidence points for pairs of mappings under specific contraction conditions.
Main Methods:
- Utilizing a generalized weak contraction condition within the framework of ordered b-metric spaces.
- Applying fixed point theorems and related techniques.
Main Results:
- Established the existence and uniqueness of fixed points for single mappings.
- Demonstrated the existence of coincidence and coupled coincidence points for pairs of mappings.
- Provided illustrative examples to validate the theoretical findings.
Conclusions:
- The study extends existing fixed point theory results to ordered b-metric spaces.
- The generalized weak contraction is effective for proving fixed point theorems in this setting.
- The findings offer valuable insights for further research in nonlinear analysis.
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