Some New Results in Extended Cone \(b\)-Metric Space
DOI:
https://doi.org/10.26713/cma.v15i2.2591Keywords:
Cone metric space, Extended cone b-metric space, Fixed point, CompletenessAbstract
The main aspect of this paper is to investigate some topological properties and Kannan-type contractions in extended cone b-metric spaces. Additionally, we have imposed some extra conditions such that a sequence in an extended cone b-metric space becomes a Cauchy sequence. Furthermore, in order to achieve new results the concept of asymptotic regularity has also been utilized.
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A. Aghajani, M. Abbas and J. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, Mathematica Slovaca 64(4) (2014), 941 – 960, DOI: 10.2478/s12175-014-0250-6.
H. Aydi, A. Felhi, T. Kamran, E. Karapinar and M. Usman, On nonlinear contractions in new extended b-metric spaces, Applications and Applied Mathematics: An International Journal (AAM) 14(1) (2019), Article 37, URL: https://digitalcommons.pvamu.edu/aam/vol14/iss1/37.
A. Azam and M. Arshad, Kannan fixed point theorem on generalized metric spaces, Journal of Nonlinear Sciences and Applications 1(1) (2008), 45 – 48, DOI: 10.22436/jnsa.001.01.07.
I. A. Bakhtin, The contraction mapping principle in almost metric spaces, Functional Analysis 30 (1989), 26 – 37.
S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fundamenta Mathematicae 3 (1922), 133 – 181, DOI: 10.4064/fm-3-1-133-181.
S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti del Seminario Matematico e Fisico dell’Universita di Modena e Reggio Emilia 46 (1998), 263 – 276.
A. Das and T. Beg, Some fixed point theorems in extended cone b-metric spaces, Communications in Mathematics and Applications 13(2) (2022), 647 – 659, DOI: 10.26713/cma.v13i2.1768.
L.-G. Huang and X. Zhang, Cone metric space and fixed point theorems of contractive mapping, Journal of Mathematical Analysis and Applications 322(2) (2007), 1468 – 1476, DOI: 10.1016/j.jmaa.2005.03.087.
N. Hussian and M. H. Shah, KKM mappings in cone b-metric spaces, Computers & Mathematics with Applications 62(4) (2011), 1677 – 1684, DOI: 10.1016/j.camwa.2011.06.004.
T. Kamran, M. Samreen and A. Ul-Qurat, A generalization of b-metric space and some fixed point theorems, Mathematics 5(2) (2017), 19, DOI: 10.3390/math5020019.
R. Kannan, Some results on fixed points, Bulletin of the Calcutta Mathematical Society 60 (1968), 71 – 76.
G. Rano, T. Bag and S. K. Samanta, Fuzzy metric space and generating space of quasi-metric family, Annals of Fuzzy Mathematics and Informatics 11(2) (2016), 183 – 195, URL: http://www.afmi.or.kr/papers/2016/Vol-11_No-02/PDF/AFMI-11-2(183-195)-H-150506R1.pdf.
Sh. Rezapour, M. Derafshpour and R. Hamlbarani, A review on topological properties of cone metric spaces, in: Proceedings of the International Conference on Analysis, Topology and Applications 2008 (ATA’08), Technical Faculty, Cacak, University of Kragujevac Vrnjacka Banja, Serbia, May 30 - June 4, 2008, URL: http://at.yorku.ca/c/a/w/q/04.htm.
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