BibTex RIS Kaynak Göster

A NEW APPROACH TO THE CONCEPT OF AI STATISTICAL CONVERGENCE WITH THE NUMBER OF ALPHA

Yıl 2018, Cilt: 67 Sayı: 1, 37 - 45, 01.02.2018
https://doi.org/10.1501/Commua1_0000000828

Öz

Abstract. Following a very recent approach, we generalize recently introduced summability method, namely, I-statisticalconvergence. We use an infinite matrix of complex numbers and an a number to do this generalization. We call this new convergence as A^I statistical convergence of order a with respect to a sequence of modulus functions. We also define two new spaces by using strong convergence and Ces·ro summability and after giving these descriptions, we investigate their relationship and we obtain some result

Kaynakça

  • Anastassiou, G. A. and Duman, O., Statistical Korovkin theory for multivariate stochastic processes, Stoch. Anal. Appl. 28 (2010), no. 4, 648-661.
  • Bhunia, S., Das, P. and Pal, S. K., Restricting statistical convergence, Acta Mathematica Hungarica 13 4 (2012), 153-161.
  • Bilgin, T., Lacunary strong A-convergence with respect to a modulus, Mathematica XLVI(4) (2001), 39-46.
  • Çolak, R., Statistical convergence of order , Modern methods in analysis and its applications, New Delhi: Anamaya Pub.(2010), 121-129.
  • Çolak, R. and Bekta¸s, Ç. A.,-statistical convergence of order ;Acta Mathematica Scientia. Series B. English Edition 31 (2011), n. 3, 953-959.
  • Das, P., Sava¸s, E. and Ghosal, S., On generalized of certain summability methods using ideals, Appl. Math. Letter 36 (2011), 1509-1514.
  • Das, P. and Sava¸s, E., On I statistical and I-lacunary statistical convergence of order a, Bull. Irani. Math. Soc. 40 (2) (2014), 459–472.
  • Erdös, P and Tenenbaum, G., Sur les densities de certaines suites d’entiers, Proc. London. Math. Soc.3(59), (1989), 417-438.
  • Et, M., Altın, Y. and Çolak, R., Almost statistical convergence of order ;Acta Scientiarum, Maringá 37 (2015), no:1, 55-61.
  • Fast, H., Sur la convergence statistique, Colloquium Mathematicum 2 (1951), 241-244.
  • Freedman, A.R., Sember, J. and Raphael, M., Some Cesàro-type summability spaces, Proc. London Math. Soc. (3) 37 no. 3 (1978), 508–520.
  • Gadjiev, A. D. and Orhan, C., Some approximation theorems via statistical convergence, Rocky Mountain J. Math. 32 (2002), no. 1, 129-138.
  • Ghosal, S., Weighted statistical convergence of order Egyptian Mathematical Society 24 (2016), 60–67. and its applications, Journal of the Gümü¸s, H. and Sava¸s, E., On SL(I)Asymptotically Statistical Equivalent Sequences, Nu- merical Analysis and Applied Mathematics 1479 (2012), 936-941.
  • Kostyrko, P., T. Šalát, T. and Wilezy´nski, W., I Convergence, Real Anal. Exchange, 26(2) (2000), 669-686.
  • Miller, H. I., A measure theoretical subsequence characterization of statistical convergence, Trans. of the Amer. Math. Soc.Vol. 347, No.5, (1995), 1811-1819. Mursaleen, M.
  • Pandoh, S. and Raj, K., Applications of statistical convergence in intuitionistic fuzzy nnormed spaces, J. Inequal. Spec. Funct. 6 (2015), no.4, 1-10.
  • Sakao¼glu, ·I. and Ünver, M., Statistical approximation for multivariable integrable functions, Miskolc Math. Notes 13 (2012), no.2, 485-491.
  • Sava¸s, E., Strong almost convergence and almost statistically convergence, Hokkaido Math. J. 21 (2000), 531-536.
  • Schoenberg, I. J., The integrability of certain functions and related summability methods, The American Mathematical Monthly 66 (1959), 361-375.
  • Steinhaus, H., Sur la convergence ordinaire et la convergence asymptotique, Colloquium Ath- ematicum 2 (1951), 73-74.
  • ¸Sengül, H. and Et, M., On lacunary statistical convergence of order , Acta Math. Sci. Ser. B Engl. Ed. 34 (2014),no.2, 473-482.
  • Yamancı, U., Gürdal, M. and Saltan, S., A-statistical convergence with respect to a sequence of modulus functions, Contemporary Analysis and Applied Mathematics 2 (2014), No.1, 136
  • Zygmund, A., Trigonometric Series, Cam. Uni. Press, Cambridge, UK., (1979).
  • Current address : Ha…ze Gümü¸s, Necmettin Erbakan University Faculty of Eregli Education Department of Math. Education, Eregli, Konya, Turkey E-mail address : hgumus@konya.edu.tr
Yıl 2018, Cilt: 67 Sayı: 1, 37 - 45, 01.02.2018
https://doi.org/10.1501/Commua1_0000000828

Öz

Kaynakça

  • Anastassiou, G. A. and Duman, O., Statistical Korovkin theory for multivariate stochastic processes, Stoch. Anal. Appl. 28 (2010), no. 4, 648-661.
  • Bhunia, S., Das, P. and Pal, S. K., Restricting statistical convergence, Acta Mathematica Hungarica 13 4 (2012), 153-161.
  • Bilgin, T., Lacunary strong A-convergence with respect to a modulus, Mathematica XLVI(4) (2001), 39-46.
  • Çolak, R., Statistical convergence of order , Modern methods in analysis and its applications, New Delhi: Anamaya Pub.(2010), 121-129.
  • Çolak, R. and Bekta¸s, Ç. A.,-statistical convergence of order ;Acta Mathematica Scientia. Series B. English Edition 31 (2011), n. 3, 953-959.
  • Das, P., Sava¸s, E. and Ghosal, S., On generalized of certain summability methods using ideals, Appl. Math. Letter 36 (2011), 1509-1514.
  • Das, P. and Sava¸s, E., On I statistical and I-lacunary statistical convergence of order a, Bull. Irani. Math. Soc. 40 (2) (2014), 459–472.
  • Erdös, P and Tenenbaum, G., Sur les densities de certaines suites d’entiers, Proc. London. Math. Soc.3(59), (1989), 417-438.
  • Et, M., Altın, Y. and Çolak, R., Almost statistical convergence of order ;Acta Scientiarum, Maringá 37 (2015), no:1, 55-61.
  • Fast, H., Sur la convergence statistique, Colloquium Mathematicum 2 (1951), 241-244.
  • Freedman, A.R., Sember, J. and Raphael, M., Some Cesàro-type summability spaces, Proc. London Math. Soc. (3) 37 no. 3 (1978), 508–520.
  • Gadjiev, A. D. and Orhan, C., Some approximation theorems via statistical convergence, Rocky Mountain J. Math. 32 (2002), no. 1, 129-138.
  • Ghosal, S., Weighted statistical convergence of order Egyptian Mathematical Society 24 (2016), 60–67. and its applications, Journal of the Gümü¸s, H. and Sava¸s, E., On SL(I)Asymptotically Statistical Equivalent Sequences, Nu- merical Analysis and Applied Mathematics 1479 (2012), 936-941.
  • Kostyrko, P., T. Šalát, T. and Wilezy´nski, W., I Convergence, Real Anal. Exchange, 26(2) (2000), 669-686.
  • Miller, H. I., A measure theoretical subsequence characterization of statistical convergence, Trans. of the Amer. Math. Soc.Vol. 347, No.5, (1995), 1811-1819. Mursaleen, M.
  • Pandoh, S. and Raj, K., Applications of statistical convergence in intuitionistic fuzzy nnormed spaces, J. Inequal. Spec. Funct. 6 (2015), no.4, 1-10.
  • Sakao¼glu, ·I. and Ünver, M., Statistical approximation for multivariable integrable functions, Miskolc Math. Notes 13 (2012), no.2, 485-491.
  • Sava¸s, E., Strong almost convergence and almost statistically convergence, Hokkaido Math. J. 21 (2000), 531-536.
  • Schoenberg, I. J., The integrability of certain functions and related summability methods, The American Mathematical Monthly 66 (1959), 361-375.
  • Steinhaus, H., Sur la convergence ordinaire et la convergence asymptotique, Colloquium Ath- ematicum 2 (1951), 73-74.
  • ¸Sengül, H. and Et, M., On lacunary statistical convergence of order , Acta Math. Sci. Ser. B Engl. Ed. 34 (2014),no.2, 473-482.
  • Yamancı, U., Gürdal, M. and Saltan, S., A-statistical convergence with respect to a sequence of modulus functions, Contemporary Analysis and Applied Mathematics 2 (2014), No.1, 136
  • Zygmund, A., Trigonometric Series, Cam. Uni. Press, Cambridge, UK., (1979).
  • Current address : Ha…ze Gümü¸s, Necmettin Erbakan University Faculty of Eregli Education Department of Math. Education, Eregli, Konya, Turkey E-mail address : hgumus@konya.edu.tr
Toplam 24 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

Hafize Gümüş Bu kişi benim

Yayımlanma Tarihi 1 Şubat 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 67 Sayı: 1

Kaynak Göster

APA Gümüş, H. (2018). A NEW APPROACH TO THE CONCEPT OF AI STATISTICAL CONVERGENCE WITH THE NUMBER OF ALPHA. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 67(1), 37-45. https://doi.org/10.1501/Commua1_0000000828
AMA Gümüş H. A NEW APPROACH TO THE CONCEPT OF AI STATISTICAL CONVERGENCE WITH THE NUMBER OF ALPHA. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Şubat 2018;67(1):37-45. doi:10.1501/Commua1_0000000828
Chicago Gümüş, Hafize. “A NEW APPROACH TO THE CONCEPT OF AI STATISTICAL CONVERGENCE WITH THE NUMBER OF ALPHA”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67, sy. 1 (Şubat 2018): 37-45. https://doi.org/10.1501/Commua1_0000000828.
EndNote Gümüş H (01 Şubat 2018) A NEW APPROACH TO THE CONCEPT OF AI STATISTICAL CONVERGENCE WITH THE NUMBER OF ALPHA. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67 1 37–45.
IEEE H. Gümüş, “A NEW APPROACH TO THE CONCEPT OF AI STATISTICAL CONVERGENCE WITH THE NUMBER OF ALPHA”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 67, sy. 1, ss. 37–45, 2018, doi: 10.1501/Commua1_0000000828.
ISNAD Gümüş, Hafize. “A NEW APPROACH TO THE CONCEPT OF AI STATISTICAL CONVERGENCE WITH THE NUMBER OF ALPHA”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67/1 (Şubat 2018), 37-45. https://doi.org/10.1501/Commua1_0000000828.
JAMA Gümüş H. A NEW APPROACH TO THE CONCEPT OF AI STATISTICAL CONVERGENCE WITH THE NUMBER OF ALPHA. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2018;67:37–45.
MLA Gümüş, Hafize. “A NEW APPROACH TO THE CONCEPT OF AI STATISTICAL CONVERGENCE WITH THE NUMBER OF ALPHA”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 67, sy. 1, 2018, ss. 37-45, doi:10.1501/Commua1_0000000828.
Vancouver Gümüş H. A NEW APPROACH TO THE CONCEPT OF AI STATISTICAL CONVERGENCE WITH THE NUMBER OF ALPHA. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2018;67(1):37-45.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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