A New Approach to the Study of Fixed Point Theory for Simulation Functions

Farshid Khojasteh, Satish Shukla, Stojan Radenović

Let $(X,d)$ be a metric space and $T:X\to X$ be a mapping. In this work, we introduce the mapping $\zeta:[0,\infty) \times[0,\infty)\to \Bbb R$, called the simulation function and the notion of $\cal Z$-contraction with respect to $\zeta$ which generalize the Banach contraction principle and unify several known types of contractions involving the combination of $d(Tx,Ty)$ and $d(x,y)$. The related fixed point theorems are also proved.