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Fixed Points of Sequence of Ćirić Generalized Contractions of Perov Type

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Abstract

Perov used the concept of vector valued metric space and obtained a Banach type fixed point theorem on such a complete generalized metric space. In this article, we study fixed point results for the new extensions of sequence of Ćirić generalized contractions on cone metric space, and we give some generalized versions of the fixed point theorem of Perov. The theory is illustrated with some examples. It is worth mentioning that the main result in this paper could not be derived from Ćirić’s result by the scalarization method, and hence indeed improves many recent results in cone metric spaces.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, Niš, 18000, Serbia

    Dejan Ilić, Marija Cvetković & Vladimir Rakočević

  2. Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Trg Dositeja Obradovića 4, Novi Sad, 21000, Serbia

    Ljiljana Gajić

Authors
  1. Dejan Ilić
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  2. Marija Cvetković
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  3. Ljiljana Gajić
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  4. Vladimir Rakočević
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Corresponding author

Correspondence to Marija Cvetković.

Additional information

Supported by Grant No. 174025 of the Ministry of Science, Technology and Development, Republic of Serbia.

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Ilić, D., Cvetković, M., Gajić, L. et al. Fixed Points of Sequence of Ćirić Generalized Contractions of Perov Type. Mediterr. J. Math. 13, 3921–3937 (2016). https://doi.org/10.1007/s00009-016-0724-6

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  • DOI: https://doi.org/10.1007/s00009-016-0724-6

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