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Funktsional. Anal. i Prilozhen., 2012, Volume 46, Issue 1, Pages 75–79 (Mi faa3057)  

This article is cited in 20 scientific papers (total in 20 papers)

Brief communications

Quasi-Contractions on a Nonnormal Cone Metric Space

L. Gajića, V. Rakočevićb

a University of Novi Sad
b University of Nis, Faculty of Sciences and Mathematics

Abstract: Ilić and Rakočević [Appl. Math. Lett., 22:5 (2009), 728–731] proved a fixed point theorem for quasi-contractive mappings on cone metric spaces when the underlying cone is normal. Recently, Z. Kadelburg, S. Radenović, and V. Rakočević obtained a similar result without using the normality condition but only for a contractive constant $\lambda\in(0,1/2)$ [Appl. Math. Lett., 22:11 (2009), 1674–1679]. In this note, using a new method of proof, we prove this theorem for any contractive constant $\lambda \in (0,1)$.

Keywords: fixed point, cone metric space, quasi-contraction

DOI: https://doi.org/10.4213/faa3057

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English version:
Functional Analysis and Its Applications, 2012, 46:1

Bibliographic databases:

UDC: 517.988
Received: 18.04.2010

Citation: L. Gajić, V. Rakočević, “Quasi-Contractions on a Nonnormal Cone Metric Space”, Funktsional. Anal. i Prilozhen., 46:1 (2012), 75–79

Citation in format AMSBIB
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\by L.~Gaji\'c, V.~Rakočevi\'c
\paper Quasi-Contractions on a Nonnormal Cone Metric Space
\jour Funktsional. Anal. i Prilozhen.
\yr 2012
\vol 46
\issue 1
\pages 75--79
\mathnet{http://mi.mathnet.ru/faa3057}
\crossref{https://doi.org/10.4213/faa3057}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2961743}
\zmath{https://zbmath.org/?q=an:06207344}
\elib{https://elibrary.ru/item.asp?id=20730644}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Liu Hao, Xu Shaoyuan, “Fixed point theorems of quasicontractions on cone metric spaces with Banach algebras”, Abstract Appl. Anal., 2013, 187348, 5 pp.  crossref  mathscinet  zmath  isi  scopus
    2. Shi Lu, Xu Shaoyuan, “Common fixed point theorems for two weakly compatible self-mappings in cone $b$-metric spaces”, Fixed Point Theory Appl., 2013, 120, 11 pp.  crossref  mathscinet  isi  scopus
    3. M. Abbas, M. Arshad, A. Azam, “Fixed points of asymptotically regular mappings in complex-valued metric spaces”, Georgian Math. J., 20:2 (2013), 213–221  crossref  mathscinet  zmath  isi  scopus
    4. M. Cvetković, V. Rakočević, “Quasi-contraction of Perov type”, Appl. Math. Comput., 237 (2014), 712–722  crossref  mathscinet  zmath  isi  scopus
    5. P. D. Proinov, I. A. Nikolova, “Iterative approximation of fixed points of quasi-contraction mappings in cone metric spaces”, J. Inequal. Appl., 2014 (2014), 226, 14 pp.  crossref  mathscinet  zmath  isi  scopus
    6. Shaoyuan Xu, Stojan Radenović, “Fixed point theorems of generalized Lipschitz mappings on cone metric spaces over Banach algebras without assumption of normality”, Fixed Point Theory Appl., 2014, 102, 12 pp.  crossref  zmath  isi  scopus
    7. M. Cvetković, V. Rakočević, “Fisher quasi-contraction of Perov type”, J. Nonlinear Convex Anal., 16:2 (2015), 339–352  mathscinet  zmath  isi  scopus
    8. M. Cvetković, V. Rakočević, “Common fixed point results for mappings of Perov type”, Math. Nachr., 288:16 (2015), 1873–1890  crossref  mathscinet  zmath  isi  scopus
    9. M. Cvetković, V. Rakočević, “Extensions of Perov theorem”, Carpathian J. Math., 31:2 (2015), 181–188  mathscinet  zmath  isi
    10. H. Huang, Sh. Xu, H. Liu, S. Radenović, “Fixed point theorems and $T$-stability of Picard iteration for generalized Lipschitz mappings in cone metric spaces over Banach algebras”, J. Comput. Anal. Appl., 20:5 (2016), 869–888  mathscinet  zmath  isi
    11. D. Ilić, M. Cvetković, L. Gajić, V. Rakočević, “Fixed points of sequence of Ćirić generalized contractions of Perov type”, Mediterr. J. Math., 13:6 (2016), 3921–3937  crossref  mathscinet  zmath  isi  scopus
    12. M. Cvetković, “Operatorial contractions on solid cone metric spaces”, J. Nonlinear Convex Anal., 17:7 (2016), 1399–1408  mathscinet  zmath  isi
    13. J. Yin, Q. Yan, T. Wang, L. Liu, “Tripled coincidence points for mixed comparable mappings in partially ordered cone metric spaces over Banach algebras”, J. Nonlinear Sci. Appl., 9:4 (2016), 1590–1599  crossref  mathscinet  zmath  isi
    14. H. Huang, S. Radenović, G. Deng, “A sharp generalization on cone $b$-metric space over Banach algebra”, J. Nonlinear Sci. Appl., 10:2 (2017), 429–435  crossref  mathscinet  isi
    15. Sh. Xu, B. Z. Popović, S. Radenović, “Fixed point results for generalized $g$-quasi-contractions of Perov-type in cone metric spaces over Banach algebras without the assumption of normality”, J. Comput. Anal. Appl., 22:4 (2017), 648–671  mathscinet  isi
    16. S. Radenović, F. Vetro, “Some remarks on Perov type mappings in cone metric spaces”, Mediterr. J. Math., 14:6 (2017), UNSP 240, 15 pp.  crossref  mathscinet  isi  scopus
    17. Sh. Xu, S. Chen, S. Aleksić, “Fixed point theorems for generalized quasi-contractions in cone $b$-metric spaces over Banach algebras without the assumption of normality with applications”, Int. J. Nonlinear Anal. Appl., 8:2 (2017), 335–353  crossref  zmath  isi
    18. M. Cvetković, “On the equivalence between Perov fixed point theorem and Banach contraction principle”, Filomat, 31:11, SI (2017), 3137–3146  crossref  mathscinet  isi  scopus
    19. S. M. Aghayan, A. Zireh, A. Ebadian, “Common best proximity point theorems on cone $b$-metric spaces over Banach algebras”, Gazi U. J. Sci., 30:2 (2017), 159–172  isi
    20. G. Wu, L. Yang, “Some fixed point theorems on cone 2-metric spaces over Banach algebras”, J. Fixed Point Theory Appl., 20:3 (2018), UNSP 108, 19 pp.  crossref  mathscinet  isi  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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