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Generalized Contractions in Partially Ordered Metric Space with Rational Expressions and Related Fixed Point Results

Muhammed Raji1, Laxmi Rathour2,, Vinay Singh2, Mutalib Sadiq3, Lakshmi Narayan Mishra4, Vishnu Narayan Mishra5

1Department of Mathematics, Confluence University of Science and Technology, Osara, Kogi State, Nigeria

2Department of Mathematics, National Institute of Technology, Chaltlang, Aizawl 796 012, Mizoram, India

3Department of Mathematics, Federal University Lokoja, Nigeria

4Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632 014, Tamil Nadu, India

5Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, Madhya Pradesh 484 887, India

American Journal of Applied Mathematics and Statistics. 2024, 12(4), 80-85. DOI: 10.12691/ajams-12-4-2
Received October 16, 2024; Revised November 18, 2024; Accepted November 25, 2024

Abstract

This paper aims to prove the existence and uniqueness of some fixed point for nonlinear contractive mappings in the setting of metric spaces and partially ordered metrics spaces satisfying a contraction condition of rational type. These contributions extend the existing literature on metric spaces and fixed point theory. Through illustrative examples, we showcase the practical applicability of our proposed notions and results, demonstrating their effectiveness in real-world scenarios.

Keywords:

Partially ordered metric space, Fixed point, Rational contractions, Monotone property
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