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Year 2022, Volume: 10 Issue: 1, 87 - 91, 15.04.2022

Bayram Sözbir , Selma Altundağ

Abstract

References

  • [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

Year 2022, Volume: 10 Issue: 1, 87 - 91, 15.04.2022

Bayram Sözbir , Selma Altundağ

Abstract

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.

Keywords

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

References

  • [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.
There are 27 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Bayram Sözbir

Selma Altundağ

Publication Date April 15, 2022
Submission Date August 18, 2021
Acceptance Date November 18, 2021
Published in Issue Year 2022 Volume: 10 Issue: 1

Cite

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. April 2022;10(1):87-91.
Chicago Sözbir, Bayram, and Selma Altundağ. “On Statistical Convergence and Lacunary Statistical Convergence of Weight $g$ on Time Scales”. Konuralp Journal of Mathematics 10, no. 1 (April 2022): 87-91.
EndNote Sözbir B, Altundağ S (April 1, 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 and S. Altundağ, “On Statistical Convergence and Lacunary Statistical Convergence of Weight $g$ on Time Scales”, Konuralp J. Math., vol. 10, no. 1, pp. 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 (April 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 and Selma Altundağ. “On Statistical Convergence and Lacunary Statistical Convergence of Weight $g$ on Time Scales”. Konuralp Journal of Mathematics, vol. 10, no. 1, 2022, pp. 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.
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