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Lacunary 𝐈𝝈-Asimptotik Denklik

Yıl 2017, Cilt: 17 Sayı: 3, 899 - 905, 29.12.2017

Uğur Ulusu

Öz

Bu çalışmada, reel sayı dizileri için lacunary 𝐈𝜎-asimptotik denklik, lacunary 𝜎-asimptotik denklik ve kuvvetli lacunary 𝜎-asimptotik 𝑝-denklik kavramları tanımlandı. Ayrıca, bu yeni denklik kavramları arasındaki ilişkiler verilerek, bu kavramların Savaş ve Patterson (2006) tarafından çalışılmış olan 𝑆𝜎𝜃-asimptotik denklik kavramı ile ilişkisinden bahsedildi.

Anahtar Kelimeler

Asimptotik denklik İstatistiksel yakınsaklık Lacunary dizi 𝐈-yakınsaklık İnvaryant yakınsaklık.

Kaynakça

  • Fast, H., 1951. Sur la convergence statistique. Colloquium Mathematicum, 2, 241--244.
  • Fridy, J. A. and Orhan, C., 1993. Lacunary statistical convergence. Pacific Journal of Mathematics, 160(1), 43--51.
  • Kostyrko, P., Macaj, M., Šalát, T. and Sleziak, M., 2005. 𝐈-Convergence and Extermal 𝐈-limits points. Mathematica Slovaca, 55, 443--464.
  • Kostyrko, P., Šalát, T. and Wilczyński, W., 2000. 𝐈-Convergence. Real Analysis Exchange, 26(2), 669--686.
  • Marouf, M., 1993. Asymptotic equivalence and summability. International Journal of Mathematics and Mathematical Sciences, 16(4), 755--762.
  • Mursaleen, M., 1979. On finite matrices and invariant means. Indian Journal of Pure and Applied Mathematics, 10, 457--460.
  • Mursaleen, M., 1983. Matrix transformation between some new sequence spaces. Houston Journal of Mathematics, 9, 505--509.
  • Mursaleen, M. and Edely, O. H. H., 2009. On the invariant mean and statistical convergence. Applied Mathematics Letters, 22(11), 1700--1704.
  • Nuray, F. and Savaş, E., 1994. Invariant statistical convergence and 𝐴-invariant statistical convergence. Indian Journal of Pure and Applied Mathematics, 25(3), 267--274.
  • Nuray, F., Gök, H. and Ulusu, U., 2011. 𝐈𝜎-convergence. Mathematical Communications, 16, 531--538.
  • Pancaroğlu, N. and Nuray, F., 2013. Statistical lacunary invariant summability. Theoretical Mathematics and Applications, 3(2), 71--78.
  • Patterson, R. F., 2003. On asymptotically statistically equivalent sequences. Demostratio Mathematica, 36(1), 149--153.
  • Patterson, R. F. and Savaş, E., 2006. On asymptotically lacunary statistically equivalent sequences. Thai Journal of Mathematics, 4(2), 267--272.
  • Raimi, R. A., 1963. Invariant means and invariant matrix methods of summability. Duke Mathematical Journal, 30(1), 81--94.
  • Savaş, E., 1989a. Some sequence spaces involving invariant means. Indian Journal of Mathematics, 31, 1--8.
  • Savaş, E., 1989b. Strongly 𝜎-convergent sequences. Bulletin of Calcutta Mathematical Society, 81, 295--300.
  • Savaş, E., 2013. On 𝐈-asymptotically lacunary statistical equivalent sequences. Advances in Difference Equations, 111(2013), 7 pages. doi:10.1186/1687-1847-2013-111.
  • Savaş, E. and Nuray, F., 1993. On 𝜎-statistically convergence and lacunary 𝜎-statistically convergence. Mathematica Slovaca, 43(3), 309--315.
  • Savaş, E. and Patterson, R. F., 2006. 𝜎-asymptotically lacunary statistical equivalent sequences. Central European Journal of Mathematics, 4(4), 648--655.
  • Savaş, R. and Başarır, M., 2006. (𝜎,𝜆)-asymptotically statistical equivalent sequences. Filomat, 20(1), 35--42.
  • Schaefer, P., 1972. Infinite matrices and invariant means. Proceedings of the American Mathematical Society, 36, 104--110.
  • Ulusu, U., (yayın aşamasında). Asymptotically ideal invariant equivalence.
  • Ulusu, U. and Nuray, F., (yayın aşamasında). Lacunary 𝐈𝜎-convergence.

Yıl 2017, Cilt: 17 Sayı: 3, 899 - 905, 29.12.2017

Uğur Ulusu

Öz

Kaynakça

  • Fast, H., 1951. Sur la convergence statistique. Colloquium Mathematicum, 2, 241--244.
  • Fridy, J. A. and Orhan, C., 1993. Lacunary statistical convergence. Pacific Journal of Mathematics, 160(1), 43--51.
  • Kostyrko, P., Macaj, M., Šalát, T. and Sleziak, M., 2005. 𝐈-Convergence and Extermal 𝐈-limits points. Mathematica Slovaca, 55, 443--464.
  • Kostyrko, P., Šalát, T. and Wilczyński, W., 2000. 𝐈-Convergence. Real Analysis Exchange, 26(2), 669--686.
  • Marouf, M., 1993. Asymptotic equivalence and summability. International Journal of Mathematics and Mathematical Sciences, 16(4), 755--762.
  • Mursaleen, M., 1979. On finite matrices and invariant means. Indian Journal of Pure and Applied Mathematics, 10, 457--460.
  • Mursaleen, M., 1983. Matrix transformation between some new sequence spaces. Houston Journal of Mathematics, 9, 505--509.
  • Mursaleen, M. and Edely, O. H. H., 2009. On the invariant mean and statistical convergence. Applied Mathematics Letters, 22(11), 1700--1704.
  • Nuray, F. and Savaş, E., 1994. Invariant statistical convergence and 𝐴-invariant statistical convergence. Indian Journal of Pure and Applied Mathematics, 25(3), 267--274.
  • Nuray, F., Gök, H. and Ulusu, U., 2011. 𝐈𝜎-convergence. Mathematical Communications, 16, 531--538.
  • Pancaroğlu, N. and Nuray, F., 2013. Statistical lacunary invariant summability. Theoretical Mathematics and Applications, 3(2), 71--78.
  • Patterson, R. F., 2003. On asymptotically statistically equivalent sequences. Demostratio Mathematica, 36(1), 149--153.
  • Patterson, R. F. and Savaş, E., 2006. On asymptotically lacunary statistically equivalent sequences. Thai Journal of Mathematics, 4(2), 267--272.
  • Raimi, R. A., 1963. Invariant means and invariant matrix methods of summability. Duke Mathematical Journal, 30(1), 81--94.
  • Savaş, E., 1989a. Some sequence spaces involving invariant means. Indian Journal of Mathematics, 31, 1--8.
  • Savaş, E., 1989b. Strongly 𝜎-convergent sequences. Bulletin of Calcutta Mathematical Society, 81, 295--300.
  • Savaş, E., 2013. On 𝐈-asymptotically lacunary statistical equivalent sequences. Advances in Difference Equations, 111(2013), 7 pages. doi:10.1186/1687-1847-2013-111.
  • Savaş, E. and Nuray, F., 1993. On 𝜎-statistically convergence and lacunary 𝜎-statistically convergence. Mathematica Slovaca, 43(3), 309--315.
  • Savaş, E. and Patterson, R. F., 2006. 𝜎-asymptotically lacunary statistical equivalent sequences. Central European Journal of Mathematics, 4(4), 648--655.
  • Savaş, R. and Başarır, M., 2006. (𝜎,𝜆)-asymptotically statistical equivalent sequences. Filomat, 20(1), 35--42.
  • Schaefer, P., 1972. Infinite matrices and invariant means. Proceedings of the American Mathematical Society, 36, 104--110.
  • Ulusu, U., (yayın aşamasında). Asymptotically ideal invariant equivalence.
  • Ulusu, U. and Nuray, F., (yayın aşamasında). Lacunary 𝐈𝜎-convergence.
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Bölüm Makaleler
Yazarlar

Uğur Ulusu

Yayımlanma Tarihi 29 Aralık 2017
Gönderilme Tarihi 22 Eylül 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 17 Sayı: 3

Kaynak Göster

APA Ulusu, U. (2017). Lacunary 𝐈𝝈-Asimptotik Denklik. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 17(3), 899-905.
AMA Ulusu U. Lacunary 𝐈𝝈-Asimptotik Denklik. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. Aralık 2017;17(3):899-905.
Chicago Ulusu, Uğur. “Lacunary 𝐈𝝈-Asimptotik Denklik”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 17, sy. 3 (Aralık 2017): 899-905.
EndNote Ulusu U (01 Aralık 2017) Lacunary 𝐈𝝈-Asimptotik Denklik. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 17 3 899–905.
IEEE U. Ulusu, “Lacunary 𝐈𝝈-Asimptotik Denklik”, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, c. 17, sy. 3, ss. 899–905, 2017.
ISNAD Ulusu, Uğur. “Lacunary 𝐈𝝈-Asimptotik Denklik”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 17/3 (Aralık 2017), 899-905.
JAMA Ulusu U. Lacunary 𝐈𝝈-Asimptotik Denklik. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2017;17:899–905.
MLA Ulusu, Uğur. “Lacunary 𝐈𝝈-Asimptotik Denklik”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, c. 17, sy. 3, 2017, ss. 899-05.
Vancouver Ulusu U. Lacunary 𝐈𝝈-Asimptotik Denklik. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2017;17(3):899-905.