<abstract xmlns="http://www.w3.org/1999/xhtml"> 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:<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/auom-2017-0007_001.jpg"></inline-graphic>x; y ∈ X. Here λn(I) represents the family of words with n letters from I, Vn(I) designates the family of words having at most n - 1 letters from I, while, if ω1 = ω1ω2 ... ωp, by fω we mean fω1 ⃘fω2 ⃘... ⃘ fωp. Denoting such a system by S = ((X; d); n; (fi)i∈I), one can consider the function FS : K(X) → K(X) described by <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/auom-2017-0007_002.jpg"></inline-graphic>, for all B ∈ K(X), where K(X) means the set of non-empty compact subsets of X. Our main result states that FS is a Picard operator for every iterated function system consisting of generalized convex contractions S. </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:x; y ∈ X. Here λn(I) represents the family of words with n letters from I, Vn(I) designates the family of words having at most n - 1 letters from I, while, if ω1 = ω1ω2 ... ωp, by fω we mean fω1  ⃘fω2 ⃘... ⃘ fωp. Denoting such a system by S = ((X; d); n; (fi)i∈I), one can consider the function FS : K(X) → K(X) described by , for all B ∈ K(X), where K(X) means the set of non-empty compact subsets of X. Our main result states that FS is a Picard operator for every iterated function system consisting of generalized convex contractions S.

IFSs consisting of generalized convex contractions

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"IFSs consisting of generalized convex contractions"}

In this paper we introduce the concept of iterated function system consisting of generalized convex contractions. More precisely, given n ∈ ℕ*, an iterated...

IFSs consisting of generalized convex contractions

Data publikacji: 21 wrz 2017

Zakres stron: 77 - 86

Otrzymano: 12 mar 2016

Przyjęty: 28 kwi 2016

DOI: https://doi.org/10.1515/auom-2017-0007

Słowa kluczowe
generalized convex contractions, fixed points, iterated function systems consisting of generalized convex contractions

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

IFSs consisting of generalized convex contractions

Data publikacji: 21 wrz 2017

Zakres stron: 77 - 86

Otrzymano: 12 mar 2016

Przyjęty: 28 kwi 2016

DOI: https://doi.org/10.1515/auom-2017-0007

Słowa kluczowegeneralized convex contractions, fixed points, iterated function systems consisting of generalized convex contractions

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Słowa kluczowe
generalized convex contractions, fixed points, iterated function systems consisting of generalized convex contractions