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Fixed point theorems on multi valued mappings in b-metric spaces.
J Maria Joseph1, D Dayana Roselin2, M Marudai3
1P.G. and Research Department of Mathematics, St. Joseph's College, Tiruchirappalli, Tamil Nadu 620 002 India.
Springerplus
|March 31, 2016
Summary
This study proves new fixed point theorems for multi-valued functions in complete b-metric spaces. These findings advance the understanding of unique solutions in these mathematical spaces.
Area of Science:
- Mathematics
- Functional Analysis
- Topology
Background:
- Fixed point theory is crucial for solving equations in various mathematical fields.
- B-metric spaces offer a generalization of metric spaces with broader applicability.
- Multi-valued mappings present unique challenges in fixed point analysis.
Purpose of the Study:
- To establish a novel fixed point theorem for multi-valued mappings.
- To introduce and prove a common fixed point theorem for such mappings.
- To extend fixed point results within the framework of complete b-metric spaces.
Main Methods:
- Utilizing concepts from topology and functional analysis.
- Developing iterative techniques specific to multi-valued functions.
- Applying properties of complete b-metric spaces.
Main Results:
- A new fixed point theorem for multi-valued mappings in complete b-metric spaces has been successfully proven.
- A common fixed point theorem for multi-valued mappings in these spaces has also been established.
- The theorems provide conditions for the existence and uniqueness of fixed points.
Conclusions:
- The research contributes significant theoretical advancements to fixed point theory.
- The findings have potential implications for solving nonlinear equations and inclusions.
- This work expands the scope of fixed point theorems in generalized metric spaces.
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