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The aim of the present research work is to investigate the solution of Urysohn integral equation by common fixed point result in the setting of complex valued b-metric space. To obtain the objective, we used a generalized rational contraction involving control functions and a pair of self-mappings. In this way, we generalize some well-known results of literature. Some non-trivial examples are also flourished to demonstrate the innovation of our principal result. [ABSTRACT FROM AUTHOR]

The aim of the present research article is to solve the system of linear equations using common fixed point theorems in the context of bicomplex valued metric spaces. To obtain our main objective, we introduce generalized contractive conditions in bicomplex valued metric spaces and establish common fixed point theorems for self mappings. We also give a significant example to demonstrate the legitimacy of the given theorems. [ABSTRACT FROM AUTHOR]

The purpose of this article is to investigate the existence of solutions for Urysohn integral equations. To achieve our objectives, we take advantage of common fixed point results for self-mappings satisfying a generalized contraction involving control functions of two variables in the context of complex valued metric spaces. We also supply a non-trivial example to show the validity of obtained results. [ABSTRACT FROM AUTHOR]

The purpose of this article is to obtain common fixed point results in b-metric spaces for generalized rational contractions involving control functions of two variables. We provide an example to show the originality of our main result. As outcomes of our results, we derive certain fixed and common fixed point results for rational contractions presuming control functions of one variable and constants. As an application, we investigate the solution of an integral equation. [ABSTRACT FROM AUTHOR]

Metric fixed-point theory has become an essential tool in computer science, communication engineering and complex systems to validate the processes and algorithms by using functional equations and iterative procedures. The aim of this article is to obtain common fixed point results in a bicomplex valued metric space for rational contractions involving control functions of two variables. Our theorems generalize some famous results from literature. We supply an example to show the originality of our main result. As an application, we develop common fixed point results for rational contractions involving control functions of one variable in the context of bicomplex valued metric space. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to establish common fixed points of six mappings in the context of bicomplex valued metric spaces. In this way, we generalize some previous well-known results from the literature. Moreover, we provide a non-trivial example to demonstrate the authenticity of established outcomes. As an application, we investigate the solution of an Urysohn integral equation by applying our results. [ABSTRACT FROM AUTHOR]

The aim of this article is to obtain common fixed points of locally contractive mappings in the setting of bicomplex valued metric spaces. Our investigations generalize some conventional theorems of literature. Furthermore, we supply a significant example to manifest the authenticity of the proved results. As an application, we solve the solution of the integral equation by using our main result. [ABSTRACT FROM AUTHOR]

The aim of this article is to obtain common fixed point results on complex-valued extended b-metric spaces for rational contractions involving control functions of two variables. Our theorems generalize some famous results in the literature. We supply an example to show the originality of our main result. As an application, we develop common fixed point results for rational contractions involving control functions of one variable in the class of complex-valued extended b-metric spaces. [ABSTRACT FROM AUTHOR]

The aim of this article is to obtain common fixed points of set mappings defined on a family of sets endowed with a graph satisfying Θ-contraction. Our results generalize and extend various results in the existing literature. We also provide some non trivial examples to support the validity of our main results. Some applications to the construction of common fixed points of set mappings in ε-chainable metric space are also discussed. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce cyclic compatible Θ-contraction and establish some common fixed point theorems in the setting of a generating space of a b-quasi-metric family. We also apply a simple condition on the function Θ to extend the result of Samet et al. (J. Inequal. Appl. 2014; 38(2014)). With this condition, we also prove a fixed point theorem for Suzuki type Θ-contractions which generalize various results of literature. [ABSTRACT FROM AUTHOR]