Simulative Suzuki-Gerghaty Type Contraction With $\mathscr{C}$ -Class Functions and Applications

Abstract

The aim of this paper is to introduce the notion of a Suzuki-Gerghaty type contractive mapping via simulation function along with C-class functions and prove the existence of fixed point result. An example is given to show the validity of our results given herein. Moreover, we prove the existence of solution of nonlinear Hammerstein integral equation.Mathematics Subject Classification: 54H25, 47H10

On some fixed point results using CG simulation functions via w-distance with applications

“…The following are examples of simulation functions: , , , where is a lower semi continuous function with , For more examples of -simulation functions see [35] , [36] , [4] .…”

An extension of Karapinar and Sadaranganis’ result through the C-class functions by using α-admissible mapping with applications

“…However, in this article, we aim to focus our study on α-admissible mapping to generalize some significant fixed point theory results through C-class function. Again, the concept of the C-class functions proposed by Ansari (2014), contained a large class of contractions (see [12], [16], [45]). In recent times many interesting results related to fixed point theory have been established (see for example [5], [15], [22], [25], [26], [31], [33], [40], [41], [43], [46], [47], [51]).…”

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