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

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Funktsional'nyi Analiz i ego Prilozheniya, 2012, Volume 46, Issue 1, Pages 75–79
DOI: https://doi.org/10.4213/faa3057 (Mi faa3057)

This article is cited in 26 scientific papers (total in 26 papers)

Brief communications

Quasi-Contractions on a Nonnormal Cone Metric Space

L. Gajić^a, V. Rakočević^b

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

Full-text PDF (161 kB) Citations (26)

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

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.

Received: 18.04.2010

English version:
Functional Analysis and Its Applications, 2012, Volume 46, Issue 1
DOI: https://doi.org/10.1007/s10688-012-0008-2

Bibliographic databases:

Document Type: Article

UDC: 517.988

Language: Russian

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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https://www.mathnet.ru/eng/faa3057

https://doi.org/10.4213/faa3057

https://www.mathnet.ru/eng/faa/v46/i1/p75

This publication is cited in the following 26 articles:

Yan Han, Shaoyuan Xu, Hüseyin Iş{\i}k, “Fixed Points and Continuity Conditions of Generalizedb-Quasicontractions”, Journal of Function Spaces, 2022 (2022), 1
Marija Cvetković, Erdal Karap{\i}nar, Vladimir Rakočević, Seher Sultan Yeşilkaya, Springer Optimization and Its Applications, 180, Approximation and Computation in Science and Engineering, 2022, 167
Mujahid Abbas, Vladimir Rakočević, Zahra Noor, “Common fixed point results of Perov type contractive mappings in D $^{*}$ -cone metric spaces”, J Anal, 29:3 (2021), 685
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.
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
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
S. Radenović, F. Vetro, “Some remarks on Perov type mappings in cone metric spaces”, Mediterr. J. Math., 14:6 (2017), UNSP 240, 15 pp.
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
M. Cvetković, “On the equivalence between Perov fixed point theorem and Banach contraction principle”, Filomat, 31:11, SI (2017), 3137–3146
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
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
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
M. Cvetković, “Operatorial contractions on solid cone metric spaces”, J. Nonlinear Convex Anal., 17:7 (2016), 1399–1408
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
M. Cvetković, V. Rakočević, “Fisher quasi-contraction of Perov type”, J. Nonlinear Convex Anal., 16:2 (2015), 339–352
M. Cvetković, V. Rakočević, “Common fixed point results for mappings of Perov type”, Math. Nachr., 288:16 (2015), 1873–1890
M. Cvetković, V. Rakočević, “Extensions of Perov theorem”, Carpathian J. Math., 31:2 (2015), 181–188
Jiandong Yin, Tao Wang, Qi Yan, “Fixed point theorems of ordered contractive mappings on cone metric spaces over Banach algebras”, Fixed Point Theory Appl, 2015:1 (2015)
Tao Wang, Jiandong Yin, Qi Yan, “Fixed point theorems on cone 2-metric spaces over Banach algebras and an application”, Fixed Point Theory Appl, 2015:1 (2015)
M. Cvetković, V. Rakočević, “Quasi-contraction of Perov type”, Appl. Math. Comput., 237 (2014), 712–722

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Functional Analysis and Its Applications

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