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Journal of Fixed Point Theory and Applications

, Volume 19, Issue 4, pp 2873–2893 | Cite as

Fixed and best proximity points for Kannan cyclic contractions in modular function spaces

  • Atanas Ilchev
  • Boyan ZlatanovEmail author
Article

Abstract

We generalize the notion of best proximity points for cyclic contraction maps in modular function spaces about Kannan maps. We have found sufficient conditions for the existence and uniqueness of best proximity points and fixed points for cyclic Kannan maps in modular function spaces. As corollaries we get sufficient conditions for the existence and uniqueness of best proximity points and fixed points for cyclic maps in Orlicz spaces, endowed with an Orlicz function modular. We present an application of the results for solving integral equations.

Keywords

Best proximity point fixed point modular function space Orlicz space integral operator 

Mathematics Subject Classification

Primary 47H10 54H25 Secondary 45D05 46A80 

Notes

Acknowledgements

We would like to thank the unanimous reviewers for their valuable comments and suggestions. First author is partially supported by University of Plovdiv “Paisii Hilendarski” NPD Project MU17 FMI-007.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Faculty of Mathematics and InformaticsUnivesrity of Plovdiv Paisii HilendarskiPlovdivBulgaria

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