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A new approach to the study of fixed point theory for simulation functions

Khojasteh Farshid (Islamic Azad University, Arak-Branch, Department of Mathematics, Arak, Iran)
Shukla Satish (Shri Vaishnav Institute of Technology and Science, Department of Applied Mathematics, Indore, India)
Radenović Stojan (Faculty of Mechanical Engineering, Beograd)

Let (X,d) be a metric space and T: X → X be a mapping. In this work, we introduce the mapping ζ:[0,1)x[0,1) → R, called the simulation function and the notion of Z-contraction with respect to Z 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.

Keywords: Contraction mapping, Simulation function, Z-contraction, Fixed point