Some theorems on fixed points in bi-complex valued metric spaces  with an application to integral equations

A. Murali; K. Muthunagai

doi:10.46481/jnsps.2024.1750

Authors

A. Murali
School of Advanced Sciences, VIT University, Chennai-600 127, Tamil Nadu, India
K. Muthunagai
[email protected]

School of Advanced Sciences, VIT University, Chennai-600 127, Tamil Nadu, India

Keywords:

common fixed point, metric space, control functions, Rational expressions

Abstract

Recent studies have highlighted fixed point theorems in the context of bicomplex valued metric spaces, utilizing rational type contractions with coefficients defined by two-variable control functions. In our research, we extend these findings by proposing new theorems for identifying common fixed points within bicomplex valued metric spaces, employing rational type contractions characterized by three-variable control functions as coefficients. We have refined the contraction conditions presented in numerous existing theorems by substituting constants with a limited number of control functions for more versatility in bicomplex valued metric spaces. This advancement broadens the scope of several significant findings in the literature. To demonstrate the efficacy of our results, we offer compelling examples that validate our theorems. Furthermore, we apply our primary findings to effectively address the Urysohn integral equation system, showcasing the practical application of our research.

Dimensions

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