Ranganath M.
- Principal R Muddurangegowda College of Education, Gurukula Badavane, Jyothinagara, Sira Town Karnataka India
Abstract
This paper provides a concise overview of metric spaces, their fundamental properties, and the idea of continuity as it pertains to these spaces, drawing parallels to uniform continuity and convergence. Also included is a review of previous research on metric space, its generalization, and practical outcomes from studies that utilized these spaces in various applications. We introduce a fixed point theorem for mixed monotone mappings in partially ordered metric spaces, assuming weak contractility. This theorem extends current knowledge and has implications for various mathematical and applied problems. Our findings include new results that enhance the theoretical framework. Under the condition of weak contractility, we also establish a fixed point theorem for mixed monotone mappings in metric spaces with partial order. In addition to incorporating several new findings, our theory can be applied to a wide range of problem classes. We address the uniqueness of a solution for a periodic boundary value problem as an application and talk about the existence of such a solution.
Keywords: Comparative Evaluation, Fixed-Point Theorems, Metric Spaces, Logical Programming,Topology
[This article belongs to Research & Reviews: Discrete Mathematical Structures(rrdms)]
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Research & Reviews: Discrete Mathematical Structures
| Volume | 11 |
| Issue | 01 |
| Received | May 23, 2024 |
| Accepted | June 29, 2024 |
| Published | July 11, 2024 |
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