Some Coupled Fixed Point Theorems for (\psi, \phi)- contraction with Applications to Fractals

Abstract

In this paper, we obtain coupled fixed point theorem for (\psi, \phi)-contractions under some generalized conditions on the real valued functions \psi and \phi defined on (0,\infinity). Also, we present a generalized version of coupled fixed point theorem for the same (\psi, \phi)- contractions. A new approach to fractal generation using the relation between fractals and fixed points is given in light of these fixed point theorems. We establish a new type of iterated function system consisting of generalized (\psi, \phi)-contractions. We also extend those results to coupled fractals.