Journals / Sigma Mühendislik ve Fen Bilimleri Dergisi / 2019 / Cilt: 37 - Sayı: 2

LACUNARY I_σ-STATISTICAL CONVERGENCE OF COMPLEX UNCERTAIN SEQUENCE

Pages
507–520
Publication Date
2019-06-01
DOI
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

In addition, decomposition theorems and relationships among them are discussed.

📌 3 Key Takeaways

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Objective & Hypothesis:This study introduces the concepts of lacunary I_σ-statistical convergence of complex uncertain sequences: lacunary I_σ-statistical convergence almost surely (S_θ ( I_σ ).a.s.), lacunary I_σ-statistical convergence in measure, lacunary I_σ-statistical convergence in mean, lacunary I_σ-statistical convergence in distribution and lacunary I_σ-statistically convergence uniformly almost surely (S_θ ( I_σ ).u.a.s).
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Key Findings & Data:This study introduces the concepts of lacunary I_σ-statistical convergence of complex uncertain sequences: lacunary I_σ-statistical convergence almost surely (S_θ ( I_σ ).a.s.), lacunary I_σ-statistical convergence in measure, lacunary I_σ-statistical convergence in mean, lacunary I_σ-statistical convergence in distribution and lacunary I_σ-statistically convergence uniformly almost surely (S_θ ( I_σ ).u.a.s).
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Conclusion & Impact:In addition, decomposition theorems and relationships among them are discussed.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Lacunary convergence · invariant · uncertainty theory

Abstract

This study introduces the concepts of lacunary I_σ-statistical convergence of complex uncertain sequences: lacunary I_σ-statistical convergence almost surely (S_θ ( I_σ ).a.s.), lacunary I_σ-statistical convergence in measure, lacunary I_σ-statistical convergence in mean, lacunary I_σ-statistical convergence in distribution and lacunary I_σ-statistically convergence uniformly almost surely (S_θ ( I_σ ).u.a.s). In addition, decomposition theorems and relationships among them are discussed.

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Cite This Article

KİŞİ, Ö. (2019). LACUNARY I_σ-STATISTICAL CONVERGENCE OF COMPLEX UNCERTAIN SEQUENCE. Sigma Mühendislik ve Fen Bilimleri Dergisi, Cilt: 37 - Sayı: 2, 507–520. https://ajindex.com/articles/419359

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References (20)

  1. Freedman, A.R., Sember, J.J., 1981, Densities and summability. Pac. J. Math., Vol. 95, No. 2, pp., 293-305.
  2. Fast, H., 1951,
  3. Sur la convergence statistique, Collog. Math., Vol. 2, pp. 241 244. Schoenberg, I.J., 1959, The integrability of certain functions and related summability method, Am. Math. Mon., Vol. 66, pp., 361-375.
  4. Fridy, J. A., Orhan, C., 1993,
  5. Lacunary Statistical Convergence, Pacific Journal of Mathematics, Vol. 160, pp., 43-51.
  6. Kostyrko, P., Mačaj, M., Šalát, T., Sleziak, M., 2005, I-convergence and extremal I-limit points, Math. Slovaca, Vol. 55, pp., 443-464. Salát, T., Tripathy, B. C., Ziman M., 2004,
  7. On Some Properties of I-Convergence, Tatra Mt. Math. Publ., Vol. 28, pp., 279-286. Salát, T., Tripathy, B. C., Ziman M., 2005,
  8. I-Convergence Field, Ital. J. Pure Appl. Math, Vol. 17, No. 5, pp., 279-286.
  9. Das, P., Savaş E., Ghosal S. Kr., 2011, On generalized of certain summability methods using ideals, Appl. Math. Letter, Vol. 36, pp., 1509-1514.
  10. Savaş, E., Nuray, F.,1993, On 𝜎-statistically convergence and lacunary σ-statistically convergence, Mat., Vol. 43. No. 3, pp., 309-135.
  11. Pancaroğlu, N., Nuray, F., 2013, Statistical lacunary invariant summability, Theor. Math. Appl., Vol. 3, No. 2, pp., 71-78.
  12. Savaş, E., 1989, Strong σ -convergent sequences, Bull. Calcutta Math., Vol. 81, pp., 295-300.
  13. Nuray, F., Gök, H., Ulusu, H., 2011, I_σ-convergence, Math. Commun., Vol. 16, pp., 531-538.
  14. Ulusu U., Nuray, F., Lacunary I_σ-convergence, (under review). Kişi, Ö., Dündar, E., 2018, Rough I_2-lacunary statistical convergence of double sequences, Journal of Inequalities and Applications, 2018:230 https://doi.org/10.1186/s13660-018-1831-7.
  15. Dündar, E., 2016, On Rough I_2-Convergence of Double Sequences, Numerical Functional Analysis and Optimization, Vol. 37, No. 4, pp., 480-491.
  16. Dündar, E., Ulusu, U., Nuray, F., 2018, On Ideal Invariant Convergence of Double Sequences and Some Properties, Creative Mathematics and Informatics, Vol. 27, No. 2, pp., 161-169.
  17. Ulusu, U., Dündar, E., Nuray, F., 2018, Lacunary I_2-invariant convergence and some properties, International Journal of Analysis and Applications, Vol. 16, No. 3, pp., 317-327.
  18. Tortop, Ş., Dündar, E., 2018, Wijsman I_2-invariant convergence of double sequences of sets, Journal of Inequalities and Special Functions, Vol. 9, No. 4, pp., 90-100.
  19. Dündar, E., Talo, Ö., 2013, I_2-convergence of double sequences of fuzzy numbers, Iranian Journal of Fuzzy Systems, Vol. 10, No. 3, pp., 37-50.
  20. Dündar, E., Altay,