Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2022, Cilt: 10 Sayı: 1, 87 - 91, 15.04.2022

Bayram Sözbir , Selma Altundağ

Öz

Kaynakça

  • [1] Y. Altin, H. Koyunbakan and E. Yilmaz, Uniform statistical convergence on time scales, J. Appl. Math., 2014 (2014), 1–6.
  • [2] Y. Altin, B.N. Er and E. Yilmaz, Dl -Statistical boundedness on time scales, Communications in Statistics-Theory and Methods, 50(3) (2021), 738–746.
  • [3] M. Balcerzak, P. Das, M. Filipczak and J. Swaczyna, Generalized kinds of density and the associated ideals, Acta Math. Hungar., 147(1) (2015), 97–115.
  • [4] M. Bohner and A. Peterson, Dynamic equations on time scales: An introduction with applications, Birkh¨auser, Boston, 2001.
  • [5] D. Borwein, Linear functionals with strong Ces´aro Summability, J. Lond. Math. Soc., 40 (1965), 628–634.
  • [6] A. Cabada and D.R. Vivero, Expression of the Lebesgue D-integral on time scales as a usual Lebesgue integral: Application to the calculus of D-antiderivatives, Math. Comput. Model., 43(1-2) (2006), 194–207.
  • [7] J.S. Connor, The statistical and strong p-Ces`aro convergence of sequences, Analysis, 8 (1988), 47–63.
  • [8] H. Fast, Sur la convergence statistique, Colloq. Math., 2 (1951), 241–244.
  • [9] A.R. Freedman, J.J. Sember and M. Raphael, Some Ces`aro-type summability spaces, Proc. Lond. Math. Soc., 37(3) (1978), 508–520. [10] J.A. Fridy, On statistical convergence, Analysis, 5 (1985), 301–313.
  • [11] J.A. Fridy and C. Orhan, Lacunary statistical convergence, Pacific J. Math., 160 (1993), 43–51.
  • [12] G.S. Guseinov, Integration on time scales, J. Math. Anal. Appl., 285(1) (2003), 107–127.
  • [13] S. Hilger, Analysis on measure chains-a unified approach to continuous and discrete calculus, Results Math., 18(1-2) (1990), 18–56.
  • [14] F. M´oricz, Statistical limits of measurable functions, Analysis, 24(1) (2004), 1–18.
  • [15] M. Mursaleen, l-statistical convergence, Math. Slovaca, 50(1) (2000), 111–115.
  • [16] E. Savas and P. Das, On I-statistical and I-lacunary statistical convergence of weight g, Bull. Math. Anal. Appl., 11(2) (2019), 2–11.
  • [17] E. Savas¸ and R. Savas¸, On Generalized Statistical Convergence and Strongly Summable Functions of Weight g, In: Roy P., Cao X., Li XZ., Das P., Deo S. (eds) Mathematical Analysis and Applications in Modeling. ICMAAM 2018. Springer Proceedings in Mathematics & Statistics, vol 302. Springer, Singapore, 2020. https://doi.org/10.1007/978-981-15-0422-8 11.
  • [18] I.J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66 (1959), 361–375.
  • [19] M.S. Seyyidoglu and N.O. Tan, A note on statistical convergence on time scale, J. Inequal. Appl., 2012(1) (2012), 1–8.
  • [20] B. Sozbir and S. Altundag, Weighted statistical convergence on time scale, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 26(2) (2019), 137–143.
  • [21] B. Sozbir and S. Altundag, ab􀀀statistical convergence on time scales, Facta Univ. Ser. Math. Inform., 35(1) (2020), 141–150.
  • [22] B. S¨ozbir and S. Altunda˘g, On asymptotically statistical equivalent functions on time scales, Mathematical Methods in the Applied Sciences, 2021. doi: 10.1002/mma.7587.
  • [23] H.M. Srivastava and M. Et, Lacunary Statistical Convergence and Strongly Lacunary Summable Functions of Order a, Filomat, 31(6) (2017), 1573–1582.
  • [24] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math., 2(1) (1951), 73–74.
  • [25] C. Turan and O. Duman, Statistical convergence on time scales and its characterizations, Springer Proc. Math. Stat., 41 (2013), 57–71.
  • [26] C. Turan and O. Duman, Convergence methods on time scales, AIP Conf. Proc., 1558(1) (2013), 1120–1123.
  • [27] C. Turan and O. Duman, Fundamental properties of statistical convergence and lacunary statistical convergence on time scales, Filomat, 31(14) (2017), 4455–4467.
  • [28] E. Yilmaz, Y. Altin and H. Koyunbakan, l-statistical convergence on time scales, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 23(1) (2016), 69–78.

On Statistical Convergence and Lacunary Statistical Convergence of Weight $g$ on Time Scales

Yıl 2022, Cilt: 10 Sayı: 1, 87 - 91, 15.04.2022

Bayram Sözbir , Selma Altundağ

Öz

The aim of this paper is to present new notions, namely, statistical convergence and lacunary statistical convergence and strong lacunary summability of weight on time scales. Furthermore, we investigate the relationships of these concepts and give some results.

Anahtar Kelimeler

Lacunary Statistical convergence Statistical convergence Strong summability Time scales Weight of g

Kaynakça

  • [1] Y. Altin, H. Koyunbakan and E. Yilmaz, Uniform statistical convergence on time scales, J. Appl. Math., 2014 (2014), 1–6.
  • [2] Y. Altin, B.N. Er and E. Yilmaz, Dl -Statistical boundedness on time scales, Communications in Statistics-Theory and Methods, 50(3) (2021), 738–746.
  • [3] M. Balcerzak, P. Das, M. Filipczak and J. Swaczyna, Generalized kinds of density and the associated ideals, Acta Math. Hungar., 147(1) (2015), 97–115.
  • [4] M. Bohner and A. Peterson, Dynamic equations on time scales: An introduction with applications, Birkh¨auser, Boston, 2001.
  • [5] D. Borwein, Linear functionals with strong Ces´aro Summability, J. Lond. Math. Soc., 40 (1965), 628–634.
  • [6] A. Cabada and D.R. Vivero, Expression of the Lebesgue D-integral on time scales as a usual Lebesgue integral: Application to the calculus of D-antiderivatives, Math. Comput. Model., 43(1-2) (2006), 194–207.
  • [7] J.S. Connor, The statistical and strong p-Ces`aro convergence of sequences, Analysis, 8 (1988), 47–63.
  • [8] H. Fast, Sur la convergence statistique, Colloq. Math., 2 (1951), 241–244.
  • [9] A.R. Freedman, J.J. Sember and M. Raphael, Some Ces`aro-type summability spaces, Proc. Lond. Math. Soc., 37(3) (1978), 508–520. [10] J.A. Fridy, On statistical convergence, Analysis, 5 (1985), 301–313.
  • [11] J.A. Fridy and C. Orhan, Lacunary statistical convergence, Pacific J. Math., 160 (1993), 43–51.
  • [12] G.S. Guseinov, Integration on time scales, J. Math. Anal. Appl., 285(1) (2003), 107–127.
  • [13] S. Hilger, Analysis on measure chains-a unified approach to continuous and discrete calculus, Results Math., 18(1-2) (1990), 18–56.
  • [14] F. M´oricz, Statistical limits of measurable functions, Analysis, 24(1) (2004), 1–18.
  • [15] M. Mursaleen, l-statistical convergence, Math. Slovaca, 50(1) (2000), 111–115.
  • [16] E. Savas and P. Das, On I-statistical and I-lacunary statistical convergence of weight g, Bull. Math. Anal. Appl., 11(2) (2019), 2–11.
  • [17] E. Savas¸ and R. Savas¸, On Generalized Statistical Convergence and Strongly Summable Functions of Weight g, In: Roy P., Cao X., Li XZ., Das P., Deo S. (eds) Mathematical Analysis and Applications in Modeling. ICMAAM 2018. Springer Proceedings in Mathematics & Statistics, vol 302. Springer, Singapore, 2020. https://doi.org/10.1007/978-981-15-0422-8 11.
  • [18] I.J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66 (1959), 361–375.
  • [19] M.S. Seyyidoglu and N.O. Tan, A note on statistical convergence on time scale, J. Inequal. Appl., 2012(1) (2012), 1–8.
  • [20] B. Sozbir and S. Altundag, Weighted statistical convergence on time scale, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 26(2) (2019), 137–143.
  • [21] B. Sozbir and S. Altundag, ab􀀀statistical convergence on time scales, Facta Univ. Ser. Math. Inform., 35(1) (2020), 141–150.
  • [22] B. S¨ozbir and S. Altunda˘g, On asymptotically statistical equivalent functions on time scales, Mathematical Methods in the Applied Sciences, 2021. doi: 10.1002/mma.7587.
  • [23] H.M. Srivastava and M. Et, Lacunary Statistical Convergence and Strongly Lacunary Summable Functions of Order a, Filomat, 31(6) (2017), 1573–1582.
  • [24] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math., 2(1) (1951), 73–74.
  • [25] C. Turan and O. Duman, Statistical convergence on time scales and its characterizations, Springer Proc. Math. Stat., 41 (2013), 57–71.
  • [26] C. Turan and O. Duman, Convergence methods on time scales, AIP Conf. Proc., 1558(1) (2013), 1120–1123.
  • [27] C. Turan and O. Duman, Fundamental properties of statistical convergence and lacunary statistical convergence on time scales, Filomat, 31(14) (2017), 4455–4467.
  • [28] E. Yilmaz, Y. Altin and H. Koyunbakan, l-statistical convergence on time scales, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 23(1) (2016), 69–78.
Toplam 27 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Bayram Sözbir

Selma Altundağ

Yayımlanma Tarihi 15 Nisan 2022
Gönderilme Tarihi 18 Ağustos 2021
Kabul Tarihi 18 Kasım 2021
Yayımlandığı Sayı Yıl 2022 Cilt: 10 Sayı: 1

Kaynak Göster

APA Sözbir, B., & Altundağ, S. (2022). On Statistical Convergence and Lacunary Statistical Convergence of Weight $g$ on Time Scales. Konuralp Journal of Mathematics, 10(1), 87-91.
AMA Sözbir B, Altundağ S. On Statistical Convergence and Lacunary Statistical Convergence of Weight $g$ on Time Scales. Konuralp J. Math. Nisan 2022;10(1):87-91.
Chicago Sözbir, Bayram, ve Selma Altundağ. “On Statistical Convergence and Lacunary Statistical Convergence of Weight $g$ on Time Scales”. Konuralp Journal of Mathematics 10, sy. 1 (Nisan 2022): 87-91.
EndNote Sözbir B, Altundağ S (01 Nisan 2022) On Statistical Convergence and Lacunary Statistical Convergence of Weight $g$ on Time Scales. Konuralp Journal of Mathematics 10 1 87–91.
IEEE B. Sözbir ve S. Altundağ, “On Statistical Convergence and Lacunary Statistical Convergence of Weight $g$ on Time Scales”, Konuralp J. Math., c. 10, sy. 1, ss. 87–91, 2022.
ISNAD Sözbir, Bayram - Altundağ, Selma. “On Statistical Convergence and Lacunary Statistical Convergence of Weight $g$ on Time Scales”. Konuralp Journal of Mathematics 10/1 (Nisan 2022), 87-91.
JAMA Sözbir B, Altundağ S. On Statistical Convergence and Lacunary Statistical Convergence of Weight $g$ on Time Scales. Konuralp J. Math. 2022;10:87–91.
MLA Sözbir, Bayram ve Selma Altundağ. “On Statistical Convergence and Lacunary Statistical Convergence of Weight $g$ on Time Scales”. Konuralp Journal of Mathematics, c. 10, sy. 1, 2022, ss. 87-91.
Vancouver Sözbir B, Altundağ S. On Statistical Convergence and Lacunary Statistical Convergence of Weight $g$ on Time Scales. Konuralp J. Math. 2022;10(1):87-91.
 Kapak Resmi İndir
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