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

Muhammed Raji¹, Laxmi Rathour^2, , Vinay Singh², Mutalib Sadiq³, Lakshmi Narayan Mishra⁴ and 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

Cite this paper:
Muhammed Raji, Laxmi Rathour, Vinay Singh, Mutalib Sadiq, Lakshmi Narayan Mishra and Vishnu Narayan Mishra. Generalized Contractions in Partially Ordered Metric Space with Rational Expressions and Related Fixed Point Results. American Journal of Applied Mathematics and Statistics. 2024; 12(4):80-85. doi: 10.12691/ajams-12-4-2

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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