IFSs consisting of generalized convex contractions

Abstract

In this paper we introduce the concept of iterated function system consisting of generalized convex contractions. More precisely, given n ∈ ℕ*, an iterated function system consisting of generalized convex contractions on a complete metric space (X; d) is given by a finite family of continuous functions (fi)i ∈I , fi : X → X, having the property that for every ω ∈ λn(I) there exists a family of positive numbers (aω;υ)υ∈Vn(I) such that:

Keywords

• generalized convex contractions
• fixed points
• iterated function systems consisting of generalized convex contractions
• primary 28a80
• secondary 54h20