Fixed point theorems for nonlinear contractions with applications to iterated function systems

Abstract

We introduce a new type of nonlinear contraction and present some fixed point results without using continuity or semi-continuity. Our result complement, extend and generalize a number of fixed point theorems including the the well-known Boyd and Wong theorem [On nonlinear contractions, Proc. Amer. Math. Soc. 20(1969)]. Also we discuss an application to iterated function systems.

Keywords

• Suzuki type contraction
• self-similarity
• iterated function systems
• fractals