Fixed Points, Fixed Sets and Iterated Multifunction Systems for Nonself Multivalued Operators

Petruşel, Adrian; Rus, İoan A.; Şerban, Marcel-Adrian

doi:10.1007/s11228-014-0291-6

Cited by 17 publications

(3 citation statements)

References 25 publications

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“…For example, Máté [10] studied the case of weaker contractions, Leśniak [8] the case of multivalued contractions, Petruşel [14] and Dumitru [4] the case of Meir-Keeler contractions, Llorens-Fuster, Petruşel and Yao [9] the case of mixed-type contractions, Boriceanu, Bota and Petruşel [2] the case of set-valued contractions on a b-metric space, Gwóźdź-� Lukowska and Jachymski [5] the case of contractions on a metric space endowed with a directed graph and Secelean [18] the case of F -contractions. For other related results see [1,3,7,11,13,15,20,23,24].…”

Section: Introductionmentioning

confidence: 93%

Reich-type iterated function systems

Miculescu

Mihail

2015

J. Fixed Point Theory Appl.

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In this paper, we introduce the concept of Reich-type iterated function system and prove the existence and uniqueness of the attractor of such a system. Moreover, we study the properties of the canonical projection from the code space onto the attractor of such a system. We also present an iterated function system consisting of continuous Reich contractions having more than one attractor.Mathematics Subject Classification. 54H25, 28A80.

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Section: Introductionmentioning

confidence: 93%

Reich-type iterated function systems

Miculescu

Mihail

2015

J. Fixed Point Theory Appl.

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“…x∈A Tx is compact [1,2,14]. Therefore if T : X → C(X) is upper semi-continuous then T 2 x = T(Tx) = y∈Tx Ty is compact.…”

Section: Multivalued Mappingsmentioning

confidence: 99%

Remarks on ”Some new fixed point theorems for contractive and nonexpansive mappings”

Pant

Nashine

Kadelburg³

2017

Filomat

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“…See, for example, . Many existence results can be found in [6,7,21] This topic is well developed for single-valued mappings [1,3,[8][9][10]17] as well as for set-valued mappings [14][15][16]20,22,26,27]. In this work, we analyze an iterative process induced by a contractive type set-valued mapping in a complete metric space.…”

Section: Introductionmentioning

confidence: 99%