A generalization of Istratescu's fixed point theorem for convex contractions

TL;DR

This paper generalizes Istrățescu's fixed point theorem to convex contractions, establishing the existence and uniqueness of attractors for iterated function systems of convex contractions and analyzing their properties.

Contribution

It introduces the concept of iterated function systems with convex contractions and proves key properties, extending previous fixed point results.

Findings

Existence and uniqueness of attractors for convex contraction systems

Properties of the canonical projection from code space to attractor

Generalization of Istrățescu's fixed point theorem

Abstract

In this paper we prove a generalization of Istr\u{a}\c{t}escu's theorem for convex contractions. More precisely, we introduce the concept of iterated function system consisting of convex contractions and prove the existence and uniqueness of the attractor of such a system. In addition we study the properties of the canonical projection from the code space into the attractor of an iterated function system consisting of convex contractions.