Journal of Fixed Point Theory and Applications

, Volume 19, Issue 4, pp 2271–2285 | Cite as

On iterated function systems consisting of Kannan maps, Reich maps, Chatterjea type maps, and related results

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Abstract

In this paper we will point out an error in proving some results on finite iterated function systems consisting of Kannan maps, Reich maps and Chatterjea type maps. In this respect, some counter-examples are given. We also answer some open questions on iterated function systems consisting of contractive maps of Reich type and we present revisions of some theorems on iterated function systems consisting of Kannan, Reich and Chatterjea type maps, by adding a commutativity assumption on the maps.

Keywords

Fixed point Iterated map system Fractal Multi-valued map Generalized contraction 

Mathematics Subject Classification

Primary 28A80 Secondary 54H25 47H10 
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Notes

Acknowledgements

The authors are greatly indebted to anonymous reviewers for their helpful comments which improved the paper in a significant way. The first author also acknowledges members of the Dong Thap Group of Mathematical Analysis and Applications for their discussions. The second author is grateful to the European infrastructure project MADECIP Dezvoltarea Infrastructurii de Cercetare pentru Managementul Dezastrelor Bazat pe Calcul de Inalta Performanta proiect finantat prin Programul Operational Sectorial Cresterea Competitivitatii Economice AXA PRIORITARA 2 Cofinantat din Fondul European de Dezvoltare Regionala Investitii pentru viitorul dumneavoastra(POSCEE COD SMIS CSNR 48806/1862) through the Research Center of Modeling, Optimization and Simulation for the technical and scientific support during the preparation of this paper.

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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  1. 1.Institute of Research and DevelopmentDuy Tan UniversityDa Nang CityVietnam
  2. 2.Faculty of Mathematics and Information Technology Teacher EducationDong Thap UniversityCao Lanh CityVietnam
  3. 3.Department of MathematicsBabeş-Bolyai UniversityCluj-NapocaRomania
  4. 4.Academy of Romanian ScientistsBucharestRomania

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