A Note on Quasi-Statistical Convergence of Order $\alpha $ in Rectangular Cone Metric Space

A Note on Quasi-Statistical Convergence of Order $\alpha $ in Rectangular Cone Metric Space

The main purpose of this paper is to describe the quasi-statistical convergence of order $\alpha $ in the rectangular cone metric space and investigate some relations of these sequences.

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  • [1] Steinhaus, H.: Sur la convergence ordinarie et la convergence asimptotique. Colloq. Math. (2), 73-74 (1951)
  • [2] Fast, H.: Sur la convergence statistique. Colloq. Math. 2, 241-244 (1951)
  • [3] Schoenberg, I., J.: The integrability of certain functions and related summability methods. Amer. Math. Montly 86, 361-375 (1959)
  • [4] Connor, J.: The statistical and strong p-Cesaro convergence of sequences. Analysis 8, 47-63 (1988)
  • [5] Connor, J.: On strong matrix summability with respect to a modulus and statistical convergence. Canad. Math. Bull. 32, 194-198 (1989)
  • [6] Fridy, J. A.: On statistical convergence. Analysis 5, 301-313, (1985)
  • [7] Maio, G. D., Koˇcinac, L. D. R.: Statistical convergence in topology. Topol. Appl. 156, 28-45 (2008)
  • [8] Li, K., Lin, S., Ge, Y.: On statistical convergence in cone metric space. Topol. Appl. 196, 641-651 (2015)
  • [9] Turan, N., Kara, E. E., lkhan, M.: Quasi statistical convergence in cone metric spaces. Facta Univ. Ser. Math. Inform. 33(4), 613-626 (2018)
  • [10] lkhan, M., Kara, E. E.: A new type of statistical Cauchy sequence and its relation to Bourbaki completeness. Cogent Math. Stat. 5(1), 1-9 (2018)
  • [11] Ganichev, M., Kadets, V.: “Filter convergence in Banach spaces and generalized bases,” in General Topology in Banach Spaces. USA: Nova Science 61-69 (2001)
  • [12] SakaoĞlu Özgüç¸, İ., Yurdakadim, T.: On quasi-statistcal convergence. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 61(1), 11-17 (2012)
  • [13] Long-Guang, H., Xian, Z.: Cone metric space and fixed point theorems of contractive mappings. J. Math. Anal. Appl. 332(2), 1467-1475 (2007)
  • [14] Azam, A., Arshad, M., Beg, I.: Banach contraction principle on cone rectangular metric space. Appl. Anal. Discrete Math. 3, 236-241 (2009)
  • [15] Jleli, M., Samet, B.: The Kannas’s fixed point theorem in a cone rectangular metric space. J. Nonlinear Sci. Appl. 2(3), 161-167 (2009)