Multivalued fractals and generalized multivalued contractions

Chifu, Cristian; Petruşel, Adrian

doi:10.1016/j.chaos.2006.06.027

Cited by 33 publications

(13 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The aim of this paper is to help connect the results on IMSs ( [3] [4]) and on self-similar networks ([1] [2]). We add a generalization the self-similar models introduced by Barabási, Ravasz and Vicsek and we describe these using IMSs constructed by contractions.…”

Section: Preliminaries and Notationsmentioning

confidence: 99%

See 1 more Smart Citation

Cantor Type Fixed Sets of Iterated Multifunction Systems Corresponding to Self-Similar Networks

Simon¹,

Soós²

2016

View full text Add to dashboard Cite

We propose a new approach to the investigation of deterministic self-similar networks by using contractive iterated multifunction systems (briefly IMSs). Our paper focuses on the generalized version of two graph models introduced by Barabási, Ravasz and Vicsek ([1] [2]). We generalize the graph models using stars and cliques: both algorithm construct graph sequences such that the next iteration is always based on n replicas of the current iteration, where n is the size of the initial graph structure, being a star or a clique. We analyze these self-similar graph sequences using IMSs in function of the size of the initial star and clique, respectively. Our research uses the Cantor set for the description of the fixed set of these IMSs, which we interpret as the limit object of the analyzed self-similar networks.

show abstract

Section: Preliminaries and Notationsmentioning

confidence: 99%

“…Based on results known on IMSs (see [3] and [4]) let us introduce the following notations: If the functions i f are singlevalued continuous self operators on a complete metric space X, then ( ) …”

Section: Preliminaries and Notationsmentioning

confidence: 99%

Cantor Type Fixed Sets of Iterated Multifunction Systems Corresponding to Self-Similar Networks

Simon¹,

Soós²

2016

View full text Add to dashboard Cite

show abstract

“…(vi) (Andres-Górniewicz [39], Chifu and Petruşel [40].) By the -contraction condition, one obtain that the operator T is H-upper semicontinuos.…”

Section: Then By (Iii) We Get That H(f T N F T ) ≤ ψ(ε)mentioning

confidence: 99%

Fixed point theory for multivalued φ-contractions

Lazăr

2011

Fixed Point Theory Appl

View full text Add to dashboard Cite

The purpose of this paper is to present a fixed point theory for multivalued -contractions using the following concepts: fixed points, strict fixed points, periodic points, strict periodic points, multivalued Picard and weakly Picard operators; data dependence of the fixed point set, sequence of multivalued operators and fixed points, Ulam-Hyers stability of a multivalued fixed point equation, well-posedness of the fixed point problem, limit shadowing property of a multivalued operator, set-toset operatorial equations and fractal operators. Our results generalize some recent theorems given in Petruşel and Rus (The theory of a metric fixed point theorem for multivalued operators,

show abstract

“…-to consider more general domains or ranges of the iterated function systems (see, for example, [6], [10], [13], [14], [24], [30], [33] and [45]). …”

Section: Introductionmentioning

confidence: 99%

Iterated Function Systems Consisting of Generalized Convex Contractions in the Framework of Complete Strong b-metric Spaces

Georgescu

2017

Annals of West University of Timisoara - Mathematics and Computer Science

View full text Add to dashboard Cite

Abstract. The concept of generalized convex contraction was introduced and studied by V. Istrȃţescu and the notion of b -metric space was introduced by I. A. Bakhtin and S. Czerwik. In this paper we combine these two elements by studying iterated function systems consisting of generalized convex contractions on the framework of b-metric spaces. More precisely we prove the existence and uniqueness of the attractor of such a system providing in this way a generalization of Istrȃţescu's convex contractions fixed point theorem in the setting of complete strong b-metric spaces.

show abstract

Multivalued fractals and generalized multivalued contractions

Cited by 33 publications

References 18 publications

Cantor Type Fixed Sets of Iterated Multifunction Systems Corresponding to Self-Similar Networks

Cantor Type Fixed Sets of Iterated Multifunction Systems Corresponding to Self-Similar Networks

Fixed point theory for multivalued φ-contractions

Iterated Function Systems Consisting of Generalized Convex Contractions in the Framework of Complete Strong b-metric Spaces

Contact Info

Product

Resources

About