<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

Published Online: Sep 21, 2017

Page range: 77 - 86

Received: Mar 12, 2016

Accepted: Apr 28, 2016

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

Keywords
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

Published Online: Sep 21, 2017

Page range: 77 - 86

Received: Mar 12, 2016

Accepted: Apr 28, 2016

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

Keywordsgeneralized 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.

Keywords
generalized convex contractions, fixed points, iterated function systems consisting of generalized convex contractions