Weak θ-contractions and some fixed point results with applications to fractal theory

Abstract

Abstract In this paper, we define weak θ-contractions on a metric space into itself by extending θ-contractions introduced by Jleli and Samet (J. Inequal. Appl. 2014:38, 2014) and utilize the same to prove some fixed point results besides proving some relation-theoretic fixed point results in generalized metric spaces. Moreover, we give some applications to fractal theory improving the classical Hutchinson–Barnsley′s theory of iterated function systems. We also give illustrative examples to exhibit the utility of our results.

Keywords

• Fixed point
• θ-contraction
• Weak θ-contraction
• Iterated function system
• Countable iterated function system
• Attractor