c-class function

In this paper, the concept of C-class functions is used to establish the existence and uniqueness of a fixed point for a self-map of integral type within a complete metric space. The theoretical foundation is presented and the results are exemplified through a specific case. Lastly, an illustration is given to demonstrate the validity of our results.

In this manuscript, we bring into play the essence of a new class of auxiliary functions, C-class functions, and exhibited some fixed point results. Notably, in this draft, we come up with the idea of modified ZF-contractions and enquire the existence and uniqueness of fixed points of such operators in the framework of θ-metric spaces. Concerning the interpretation of the achieved results, some non-trivial examples are also studied. From obtained theorems, we derive several related fixed point results in usual metric spaces and θ-metric spaces.

In this paper we study the notion of Gerghaty type contractive mapping via simulation function along with $mathcal{C}$-class functions and prove the existence of several fixed point results in ordinary and partially ordered metric spaces. An example is given to show the validity of our results given herein. Moreover, existence of solution of two-point boundary value second order nonlinear differential equation is obtain.

In this paper, we discuss and extend some recent common fixed point results established by using φ− weakly contractive mappings. A very important step in the development of the fixed point theory was given by A.H. Ansari by the introduction of a C−class function. Using C− class functions, we generalize some known fixed point results. This type of functions is a very important class of functions which contains almost all known type contraction starting from 1922. year, respectively from famous Banach contraction principle. Three common fixed point theorems for four mappings are presented. The obtained results generalizes several existing ones in literature.We finally propose three open problems.