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Some New Results in Partial Cone $b$-Metric Space

Yıl 2020, Cilt: 3 Sayı: 2, 67 - 73, 30.06.2020

Zeynep Kalkan Aynur Şahin

https://doi.org/10.33434/cams.684102
Cited By: 2

Öz

In this paper, we introduce the concepts of the Ulam-Hyers-Rassias stability and the limit shadowing property of a fixed point problem and the $P$-property of a mapping in partial cone $b$-metric space. Also, we give such results by using the mapping which is studied by Fernandez et al.[4] in partial cone $b$-metric space and provide some numerical examples to support our results. The results presented here extend and improve some recent results announced in the current literature.

Anahtar Kelimeler

Fixed point Limit shadowing property P-property Partial cone b-metric space Ulam-Hyers-Rassias stability

Teşekkür

The authors would like to thank Prof. Metin Başarır for his valuable suggestions to improve the content of the manuscript.

Kaynakça

  • [1] S. Czerwik, Contraction mapping in b-metric space, Acta Math. Inform. Univ. Ostrav, 1 (1993), 5-11.
  • [2] N. Hussain, M. H. Shah, KKM mapping in cone b-metric spaces, Computer Math. Appl., 62 (2011), 1677-1687.
  • [3] A. Sönmez, Fixed point theorems in partial cone metric spaces, (2011), arXiv:1101.2741v1 [math. GN].
  • [4] J. Fernandez, N. Malviya, B. Fisher, The asymptotically regularity and sequences in partial cone b-metric spaces with application, Filomat, 30(10) (2016), 2749-2760.
  • [5] S. M. Ulam, Problems in Modern Mathematics, John Wiley & Sons, New York, USA, 1964.
  • [6] D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA., 27 (1941), 222-224.
  • [7] T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan., 2 (1950), 64-66.
  • [8] Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 237-300.
  • [9] I. A. Rus, Ulam stabilities of ordinary differential equation in a Banach space, Carpathian J. Math., 26(1) (2010), 103-107.
  • [10] L. Cadariu, L. Gavruta, P. Gavruta, Fixed points and generalized Hyers-Ulam stability, Abstr. Appl. Anal., 2012 (2012), Article ID 712743, 10 pages.
  • [11] L. P. Castro, R. C. Guerra, Hyers-Ulam-Rassias stability of Volterra integral equation within weighted spaces, Libertas Math. (new series), 33(2) (2013), 21-35.
  • [12] W. Sintunavarat, Generalized Ulam-Hyers stability, well-posedness and limit shadowing of the fixed point problems for $\alpha -\beta -$contraction mapping in metric space, Sci.World. J., 2014 (2014), Article ID 569174, 7 pages.
  • [13] A. Şahin, H. Arısoy, Z. Kalkan, On the stability of two functional equations arising in mathematical biology and theory of learning, Creat. Math. Inform., 28(1) (2019), 91-95.
  • [14] S. Y. Pilyugin, Sets of dynamical systems with various limit shadowing properties, J. Dynam. Differantial Equations, 19(3) (2007), 747-775.
  • [15] G. S. Jeong, B. E. Rhoades, Maps for which $F(T)=F(T^{n})$}, Fixed Point Theory Appl. 6 71-105, Nova Sci. Publ. New York, USA, 2007.
  • [16] G. S. Jeong, B. E. Rhoades, More maps for which $F(T)=F(T^{n})$}, Demonstratio Math., 40(3) (2007), 671-680.
  • [17] B. E. Rhoades, M. Abbas, Maps satisfying generalized contractive conditions of integral type for which $F(T)=F(T^{n})$}, Int. J. Pure Appl. Math. 45(2) (2008), 225-231.
  • [18] H. Huang, G. Deng, S. Radenovic, Fixed point theorems in $b$-metric spaces with applications to differential equation, J. Fixed Point Theory Appl., 20(52) (2018), 1-24.

Yıl 2020, Cilt: 3 Sayı: 2, 67 - 73, 30.06.2020

Zeynep Kalkan Aynur Şahin

https://doi.org/10.33434/cams.684102
Cited By: 2

Öz

Kaynakça

  • [1] S. Czerwik, Contraction mapping in b-metric space, Acta Math. Inform. Univ. Ostrav, 1 (1993), 5-11.
  • [2] N. Hussain, M. H. Shah, KKM mapping in cone b-metric spaces, Computer Math. Appl., 62 (2011), 1677-1687.
  • [3] A. Sönmez, Fixed point theorems in partial cone metric spaces, (2011), arXiv:1101.2741v1 [math. GN].
  • [4] J. Fernandez, N. Malviya, B. Fisher, The asymptotically regularity and sequences in partial cone b-metric spaces with application, Filomat, 30(10) (2016), 2749-2760.
  • [5] S. M. Ulam, Problems in Modern Mathematics, John Wiley & Sons, New York, USA, 1964.
  • [6] D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA., 27 (1941), 222-224.
  • [7] T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan., 2 (1950), 64-66.
  • [8] Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 237-300.
  • [9] I. A. Rus, Ulam stabilities of ordinary differential equation in a Banach space, Carpathian J. Math., 26(1) (2010), 103-107.
  • [10] L. Cadariu, L. Gavruta, P. Gavruta, Fixed points and generalized Hyers-Ulam stability, Abstr. Appl. Anal., 2012 (2012), Article ID 712743, 10 pages.
  • [11] L. P. Castro, R. C. Guerra, Hyers-Ulam-Rassias stability of Volterra integral equation within weighted spaces, Libertas Math. (new series), 33(2) (2013), 21-35.
  • [12] W. Sintunavarat, Generalized Ulam-Hyers stability, well-posedness and limit shadowing of the fixed point problems for $\alpha -\beta -$contraction mapping in metric space, Sci.World. J., 2014 (2014), Article ID 569174, 7 pages.
  • [13] A. Şahin, H. Arısoy, Z. Kalkan, On the stability of two functional equations arising in mathematical biology and theory of learning, Creat. Math. Inform., 28(1) (2019), 91-95.
  • [14] S. Y. Pilyugin, Sets of dynamical systems with various limit shadowing properties, J. Dynam. Differantial Equations, 19(3) (2007), 747-775.
  • [15] G. S. Jeong, B. E. Rhoades, Maps for which $F(T)=F(T^{n})$}, Fixed Point Theory Appl. 6 71-105, Nova Sci. Publ. New York, USA, 2007.
  • [16] G. S. Jeong, B. E. Rhoades, More maps for which $F(T)=F(T^{n})$}, Demonstratio Math., 40(3) (2007), 671-680.
  • [17] B. E. Rhoades, M. Abbas, Maps satisfying generalized contractive conditions of integral type for which $F(T)=F(T^{n})$}, Int. J. Pure Appl. Math. 45(2) (2008), 225-231.
  • [18] H. Huang, G. Deng, S. Radenovic, Fixed point theorems in $b$-metric spaces with applications to differential equation, J. Fixed Point Theory Appl., 20(52) (2018), 1-24.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Zeynep Kalkan 0000-0001-6760-9820

Aynur Şahin 0000-0001-6114-9966

Yayımlanma Tarihi 30 Haziran 2020
Gönderilme Tarihi 4 Şubat 2020
Kabul Tarihi 30 Mart 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 3 Sayı: 2

Kaynak Göster

APA Kalkan, Z., & Şahin, A. (2020). Some New Results in Partial Cone $b$-Metric Space. Communications in Advanced Mathematical Sciences, 3(2), 67-73. https://doi.org/10.33434/cams.684102
AMA Kalkan Z, Şahin A. Some New Results in Partial Cone $b$-Metric Space. Communications in Advanced Mathematical Sciences. Haziran 2020;3(2):67-73. doi:10.33434/cams.684102
Chicago Kalkan, Zeynep, ve Aynur Şahin. “Some New Results in Partial Cone $b$-Metric Space”. Communications in Advanced Mathematical Sciences 3, sy. 2 (Haziran 2020): 67-73. https://doi.org/10.33434/cams.684102.
EndNote Kalkan Z, Şahin A (01 Haziran 2020) Some New Results in Partial Cone $b$-Metric Space. Communications in Advanced Mathematical Sciences 3 2 67–73.
IEEE Z. Kalkan ve A. Şahin, “Some New Results in Partial Cone $b$-Metric Space”, Communications in Advanced Mathematical Sciences, c. 3, sy. 2, ss. 67–73, 2020, doi: 10.33434/cams.684102.
ISNAD Kalkan, Zeynep - Şahin, Aynur. “Some New Results in Partial Cone $b$-Metric Space”. Communications in Advanced Mathematical Sciences 3/2 (Haziran 2020), 67-73. https://doi.org/10.33434/cams.684102.
JAMA Kalkan Z, Şahin A. Some New Results in Partial Cone $b$-Metric Space. Communications in Advanced Mathematical Sciences. 2020;3:67–73.
MLA Kalkan, Zeynep ve Aynur Şahin. “Some New Results in Partial Cone $b$-Metric Space”. Communications in Advanced Mathematical Sciences, c. 3, sy. 2, 2020, ss. 67-73, doi:10.33434/cams.684102.
Vancouver Kalkan Z, Şahin A. Some New Results in Partial Cone $b$-Metric Space. Communications in Advanced Mathematical Sciences. 2020;3(2):67-73.

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