Research article

Deferred statistical convergence of order α in metric spaces

  • Received: 27 December 2019 Accepted: 10 April 2020 Published: 20 April 2020
  • MSC : 40A05, 40C05, 46A45

  • In this paper, the concepts of deferred statistical convergence of order α and deferred strong Cesàro summability are generalized to general metric spaces and some relations between deferred strong Cesàro summability of order α and deferred statistical convergence of order α are given in general metric spaces.

    Citation: Mikail Et, Muhammed Cinar, Hacer Sengul Kandemir. Deferred statistical convergence of order α in metric spaces[J]. AIMS Mathematics, 2020, 5(4): 3731-3740. doi: 10.3934/math.2020241

    Related Papers:

  • In this paper, the concepts of deferred statistical convergence of order α and deferred strong Cesàro summability are generalized to general metric spaces and some relations between deferred strong Cesàro summability of order α and deferred statistical convergence of order α are given in general metric spaces.



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    [1] A. Zygmund, Trigonometric Series, Cambridge University Press, Cambridge, London and New York, 1979.
    [2] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math., 2 (1951), 73-74.
    [3] H. Fast, Sur la convergence statistique, Colloq. Math., 2 (1951), 241-244. doi: 10.4064/cm-2-3-4-241-244
    [4] I. J. Schoenberg, The integrability of certain functions and related summability methods, Am. Math. Mon., 66 (1959), 361-375. doi: 10.1080/00029890.1959.11989303
    [5] B. Bilalov, T. Nazarova, On statistical convergence in metric space, Journal of Mathematics Research, 7 (2015), 37-43.
    [6] N. L. Braha, H. M. Srivastava, S. A. Mohiuddine, A Korovkin's type approximation theorem for periodic functions via the statistical summability of the generalized de la Vallée Poussin mean, Appl. Math. Comput., 228 (2014), 162-169.
    [7] M. Cinar, M. Karakas, M. Et, On pointwise and uniform statistical convergence of order α for sequences of functions, Fixed Point Theory A., 2013 (2013), 1-11. doi: 10.1186/1687-1812-2013-1
    [8] R. Colak, Modern Methods in Analysis and Its Applications, New Delhi, India: Anamaya Pub, 2010 (2010), 121-129.
    [9] J. S. Connor, The Statistical and strong p-Cesàro convergence of sequences, Analysis, 8 (1988), 47-63. doi: 10.1524/anly.1988.8.12.95
    [10] M. Et, H. Şengül, On pointwise lacunary statistical convergence of order α of sequences of function, P. Natl. A. Sci. India A., 85 (2015), 253-258.
    [11] M. Et, S. A. Mohiuddine, A. Alotaibi, On λ-statistical convergence and strongly λ-summable functions of order α, J. Inequal. Appl., 2013 (2013), 1-8. doi: 10.1186/1029-242X-2013-1
    [12] M. Et, B. C. Tripathy, A. J. Dutta, On pointwise statistical convergence of order α of sequences of fuzzy mappings. Kuwait J. Sci., 41 (2014), 17-30.
    [13] M. Et, R. Colak, Y. Altin, Strongly almost summable sequences of order α, Kuwait J. Sci., 41 (2014), 35-47.
    [14] E. Savas, M. Et, On $(\Delta _{\lambda }.{m}, I)$-statistical convergence of order α, Period. Math. Hung., 71 (2015), 135-145.
    [15] J. A. Fridy, On statistical convergence, Analysis, 5 (1985), 301-313.
    [16] M. Işık, K. E. Akbaş, On λ-statistical convergence of order α in probability, J. Inequal. Spec. Funct., 8 (2017), 57-64.
    [17] M. Işık, K. E. Et, On lacunary statistical convergence of order α in probability, AIP Conference Proceedings, 1676 (2015), 020045. doi: 10.1063/1.4930471
    [18] M. Işık, K. E. Akbaş, On asymptotically lacunary statistical equivalent sequences of order in probability, ITM Web of Conferences, 13 (2017), 01024. doi: 10.1051/itmconf/20171301024
    [19] E. Kayan, R. Colak, Y. Altin, d-statistical convergence of order α and d-statistical boundedness of order α in metric spaces, U. P. B. Sci. Bull., Series A, 80 (2018), 229-238.
    [20] M. Küçükaslan, M. Yılmaztürk, On deferred statistical convergence of sequences, Kyungpook Math. J., 56 (2016), 357-366. doi: 10.5666/KMJ.2016.56.2.357
    [21] M. Küçükaslan, U. Dğer, O. Dovgoshey, On the statistical convergence of metric-valued sequences, Ukrains'kyi Matematychnyi Zhurnal, 66 (2014), 712-720.
    [22] S. A. Mohiuddine, A. Alotaibi, M. Mursaleen, Statistical convergence of double sequences in locally solid Riesz spaces, Abstr. Appl. Anal., 2012 (2012), 1-9.
    [23] F. Nuray, λ-strongly summable and λ-statistically convergent functions, Iran. J. Sci. Technol. A., 34 (2010), 335-338.
    [24] F. Nuray, B. Aydin, Strongly summable and statistically convergent functions, Inform. Technol. Valdymas, 1 (2004), 74-76.
    [25] T. Šalát, On statistically convergent sequences of real numbers, Math. Slovaca, 30 (1980), 139-150.
    [26] H. Şengül, M. Et, On I-lacunary statistical convergence of order α of sequences of sets, Filomat 31 (2017), 2403-2412. doi: 10.2298/FIL1708403S
    [27] H. Şengül, On Wijsman I-lacunary statistical equivalence of order (η, μ), J. Inequal. Spec. Funct., 9 (2018), 92-101.
    [28] H. Şengül, On $S_{\alpha }.{\beta }\left(\theta \right)$-convergence and strong $N_{\alpha }.{\beta }\left(\theta, p\right) $-summability, J. Nonlinear Sci. Appl., 10 (2017), 5108-5115.
    [29] H. Şengül, M. Et, Lacunary statistical convergence of order (α, β) in topological groups, Creat. Math. Inform., 26 (2017), 339-344. doi: 10.37193/CMI.2017.03.11
    [30] H. M. Srivastava, M. Mursaleen, A. Khan, Generalized equi-statistical convergence of positive linear operators and associated approximation theorems, Math. Comput. Model., 55 (2012), 2040-2051. doi: 10.1016/j.mcm.2011.12.011
    [31] H. M. Srivastava, M. Et, Lacunary statistical convergence and strongly lacunary summable functions of order α, Filomat, 31 (2017), 1573-1582. doi: 10.2298/FIL1706573S
    [32] R. P. Agnew, On deferred Cesàro mean, Ann. Math., 33 (1932), 413-421. doi: 10.2307/1968524
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