FIXED POINTS FOR MULTIVALUED CONTRACTIONS IN $b$-METRIC SPACES WITH APPLICATIONS TO FRACTALS

Chifu, Cristian; Petruşel, Gabriela

doi:10.11650/tjm.18.2014.4137

Cited by 37 publications

(28 citation statements)

References 5 publications

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“…The concept of a b-metric space was introduced by Czerwik in [11]. Since then, several papers have been published on the fixed point theory of various classes of single-valued and multi-valued operators in b-metric space [3,6,7,8,9,10,11,12,13,24,29].…”

Section: Introductionmentioning

confidence: 99%

Fractals of GeneralizedF-Hutchinson Operator inb-Metric Spaces

Nazır

Silvestrov

2016

Journal of Operators

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The aim of this paper is to construct a fractal with the help of a finite family of generalized F -contraction mappings, a class of mappings more general than contraction mappings, defined in the setup of b-metric space. Consequently, we obtain a variety of results for iterated function system satisfying a different set of contractive conditions. Our results unify, generalize and extend various results in the existing literature.---------------

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Section: Introductionmentioning

confidence: 99%

Fractals of GeneralizedF-Hutchinson Operator inb-Metric Spaces

Nazır

Silvestrov

2016

Journal of Operators

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“…A. Bakhtin [4] and S. Czerwik (see [11] and [12]) in connection with some problems concerning the convergence of measurable functions with respect to measure. Among the fixed point results in the framework of b-metric spaces obtained in the last period (see, for example, [2], [6], [7], [10], [18], [19], [22], [25], [28] and the references therein, to mention just the most recent ones) we point out a Matkowski type fixed point result (in the framework of such a space X with the property that the b-metric is a continuous functional on X × X and for a b-comparison function ϕ) which is due to M. Pȃcurar (Berinde) (see [20] and [21]). …”

Section: Introductionmentioning

confidence: 99%

A generalization of Matkowski’s fixed point theorem and Istrăţescu’s fixed point theorem concerning convex contractions

Miculescu

Mihail

2017

J. Fixed Point Theory Appl.

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Abstract. In this paper we obtain a generalization of Matkowski's fixed point theorem and Istrȃţescu's fixed point theorem concerning convex contractions. More precisely, given a complete b-metric space (X, d), we prove that every continuous function f : X → X is a Picard operator, provided that there exist m ∈ N * and a comparison functionfor all x, y ∈ X. In addition, we point out that if m = 1, the continuity condition on f is not necessary and consequently, taking into account that a metric space is a b-metric space, we obtain a generalization of Matkowski's fixed point theorem. Moreover, we prove that Istrȃţescu's fixed point theorem concerning convex contractions is a particular case of our result for m = 2. By providing appropriate examples we show that the above mentioned two generalizations are effective.2010 Mathematics Subject Classification: 54H25, 47H10

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“…-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%

“…Concerning the first line of generalization, we emphasize the papers [10], [14] and [45], were iterated function systems in the setting of b-metric spaces are studied. The notion of b-metric space was introduced by I.…”

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

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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.

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FIXED POINTS FOR MULTIVALUED CONTRACTIONS IN $b$-METRIC SPACES WITH APPLICATIONS TO FRACTALS

Cited by 37 publications

References 5 publications

Fractals of GeneralizedF-Hutchinson Operator inb-Metric Spaces

Fractals of GeneralizedF-Hutchinson Operator inb-Metric Spaces

A generalization of Matkowski’s fixed point theorem and Istrăţescu’s fixed point theorem concerning convex contractions

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

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