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Lacunary 𝐈𝝈-Asimptotik Denklik

Year 2017, Volume: 17 Issue: 3, 899 - 905, 29.12.2017

Uğur Ulusu

Abstract

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.

Keywords

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

References

  • 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.

Year 2017, Volume: 17 Issue: 3, 899 - 905, 29.12.2017

Uğur Ulusu

Abstract

References

  • 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.
There are 23 citations in total.

Details

Primary Language Turkish
Journal Section Articles
Authors

Uğur Ulusu

Publication Date December 29, 2017
Submission Date September 22, 2017
Published in Issue Year 2017 Volume: 17 Issue: 3

Cite

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. December 2017;17(3):899-905.
Chicago Ulusu, Uğur. “Lacunary 𝐈𝝈-Asimptotik Denklik”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 17, no. 3 (December 2017): 899-905.
EndNote Ulusu U (December 1, 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, vol. 17, no. 3, pp. 899–905, 2017.
ISNAD Ulusu, Uğur. “Lacunary 𝐈𝝈-Asimptotik Denklik”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 17/3 (December 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, vol. 17, no. 3, 2017, pp. 899-05.
Vancouver Ulusu U. Lacunary 𝐈𝝈-Asimptotik Denklik. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2017;17(3):899-905.