Some Coupled Fixed Point Theorems for (ψ, ϕ)- contraction with Applications to Fractals

Abstract

In this paper, we obtain coupled fixed point theorem for (ψ, ϕ)-contractions under some generalized conditions on the real valued functions ψ and ϕ defined on (0,∞). Also, we present a generalized version of coupled fixed point theorem for the same (ψ, ϕ)-contractions. A new approach to fractal generation by 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 (ψ, ϕ)-contractions. We also extend those results to coupled fractals.