A new aspect to Picard operators with simulation functions

Abstract

In the present paper, considering the simulation function, we give a new class of Picard operators on complete metric spaces. We also provide a nontrivial example that shows the aforementioned class properly contains some earlier such classes.

Simulation type functions and coincidence points

“…Now, we state our first new result for the notion of Z G , -contraction. It generalizes the corresponding results of [5,8,13,16] in several directions. Theorem 2.2.…”

“…In the case that = i X (identity mapping on X) and C G = 0 we get Z-contraction of [16] (Definition 2, Theorem 2).…”

Picard-Jungck Operator for a Pair of Mappings and Simulation Type Functions

“…1+v . Now, we have that The following example shows that our Theorem 1 is a proper generalization of the corresponding results of Jungck [15], L.-de-Hierro et al [5] and of Olgun et al [16]. → as f = 2+ , g = 2 .…”

Fixed point results on θ-metric spaces via simulation functions

“…This kind of functions have attracted much attention because they are useful to express a great family of contractivity conditions that were well known in the field of fixed point theory. Later on, Olgun et al [11] provided a new class of Picard operator on complete metric spaces using the concept of generalized Z−contraction. In this exciting context, there are a lot of developments have been done in recent times [10,12].…”