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Basic inequality on a b-metric space and its applications
1Department of Basic Sciences, Faculty of Engineering, Kyushu Institute of Technology, Tobata, Kitakyushu, 804-8550 Japan.
Journal of Inequalities and Applications
|October 31, 2017
Summary
Researchers proved fundamental inequalities and fixed-point theorems in b-metric spaces. They explored conditions impacting sequence Cauchyness, distinguishing between those that imply it and those that do not.
Area of Science:
- Mathematical Analysis
- Topology
Background:
- b-metric spaces are a generalization of metric spaces with a constant 'b' greater than or equal to 1.
- Inequalities and fixed-point theorems are foundational concepts in mathematical analysis with wide applications.
Purpose of the Study:
- To establish basic inequalities within the framework of b-metric spaces.
- To investigate and prove fixed-point theorems in these spaces.
- To analyze conditions related to the convergence of sequences in b-metric spaces.
Main Methods:
- Proving fundamental inequalities specific to b-metric spaces.
- Applying fixed-point theory techniques to b-metric spaces.
- Analyzing sequence properties under different conditions.
Main Results:
- Establishment of a basic inequality in b-metric spaces.
- Demonstration of several fixed-point theorems.
- Identification of two distinct conditions affecting sequence Cauchyness.
Conclusions:
- The study contributes foundational results to the theory of b-metric spaces.
- The findings offer new insights into convergence properties of sequences.
- The distinction between the two conditions provides a nuanced understanding of Cauchyness.
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