SavedAdd your journal

Journals / Sigma Journal of Engineering and Natural Sciences / 2026 / Volume: 37 Issue: 2

LACUNARY I_σ-STATISTICAL CONVERGENCE OF COMPLEX UNCERTAIN SEQUENCE

Ömer Kişi(BARTIN UNIVERSITY)0000-0001-6844-3092
Pages
—
Publication Date
2019-06-01
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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

📌 3 Key Takeaways

🎯
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).
📊
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).
💡
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.

🔖

Cite This Article

Kişi, Ö. (2019). LACUNARY I_σ-STATISTICAL CONVERGENCE OF COMPLEX UNCERTAIN SEQUENCE. Sigma Journal of Engineering and Natural Sciences, Volume: 37 Issue: 2. https://ajindex.com/articles/1632756

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (38)

  1. Freedman, A.R., Sember, J.J., 1981, Densities and summability. Pac. J. Math., Vol. 95, No. 2, pp., 293-305. Fast, H., 1951, Sur la convergence statistique, Collog. Math., Vol. 2, pp. 241 244.
  2. Schoenberg, I.J., 1959, The integrability of certain functions and related summability method, Am. Math. Mon., Vol. 66, pp., 361-375.
  3. Fridy, J. A., Orhan, C., 1993, Lacunary Statistical Convergence, Pacific Journal of Mathematics, Vol. 160, pp., 43-51.
  4. Kostyrko, P., Mačaj, M., Šalát, T., Sleziak, M., 2005, I-convergence and extremal I-limit points, Math. Slovaca, Vol. 55, pp., 443-464.
  5. Salát, T., Tripathy, B. C., Ziman M., 2004, On Some Properties of I-Convergence, Tatra Mt. Math. Publ., Vol. 28, pp., 279-286.
  6. Salát, T., Tripathy, B. C., Ziman M., 2005, I-Convergence Field, Ital. J. Pure Appl. Math, Vol. 17, No. 5, pp., 279-286. Das, P., Savaş E., Ghosal S. Kr., 2011, On generalized of certain summability methods using ideals, Appl. Math. Letter, Vol. 36, pp., 1509-1514.
  7. Savaş, E., Nuray, F.,1993, On 𝜎-statistically convergence and lacunary σ-statistically convergence, Mat., Vol. 43. No. 3, pp., 309-135.
  8. Pancaroğlu, N., Nuray, F., 2013, Statistical lacunary invariant summability, Theor. Math. Appl., Vol. 3, No. 2, pp., 71-78.
  9. Savaş, E., 1989, Strong σ -convergent sequences, Bull. Calcutta Math., Vol. 81, pp., 295-300.
  10. Nuray, F., Gök, H., Ulusu, H., 2011, I_σ-convergence, Math. Commun., Vol. 16, pp., 531-538.
  11. Ulusu U., Nuray, F., Lacunary I_σ-convergence, (under review).
  12. 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.
  13. Dündar, E., 2016, On Rough I_2-Convergence of Double Sequences, Numerical Functional Analysis and Optimization, Vol. 37, No. 4, pp., 480-491.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. Dündar, E., Altay, B., 2012, Multipliers for bounded I_2-convergence of double sequences, Mathematical and Computer Modelling, Vol. 55, pp., 1193-1198.
  19. Pancaroğlu Akın, N., Dündar, E., Ulusu, U., 2018, Asymptotically I_σθ-statistical equivalence of sequences of sets de ned by a modulus functions, Sakarya University Journal of Science, Vol. 22, No. 6, pp., 1857-1862.
  20. Demirci, K., 2001, I-limit superior and limit inferior, Math. Commun., Vol. 6, No. 2, pp., 165-172.
  21. Liu, B., Uncertainty Theory, 2nd. ed., Springer-Verlag, Berlin, 2007.
  22. Liu, B., 2011, Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty, Springer-Verlag, Berlin.
  23. Liu, B., 2009, Theory and Practice of Uncertain Programming, 2nd edn., Springer-Verlag, Berlin.
  24. Liu, B., Chen, X., 2015, Uncertain multiobjective programming and uncertain goal programming, Journal of Uncertainty Analysis and Applications, Vol. 3, No. 10, pp., 1-8, DOI 10.1186/s40467-015-0036-6.
  25. Liu, B., 2010, Uncertainty risk analysis and uncertain reliability analysis, Journal of Uncertain Systems, Vol. 4, No. 3, pp., 163-170.
  26. Liu, B., 2011, Uncertainty logic for modelling human language, Journal of Uncertain Systems, Vol. 5, No. 1, pp., 3-20.
  27. Yao, K., Chen, X., 2013, A numberical method for solving uncertain differential equations, Journal of Intelligent & Fuzzy Systems, Vol. 25, No. 3, pp., 825-832.
  28. Gao, X., Gao, Y., Connectedness index of uncertain graphs, International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems 21(1) (2013), 127-137.
  29. Zhang, B., Peng, J., 2012, Euler index in uncertain graph, Applied Mathematics and Computation, Vol. 218, No. 20, pp., 10279-10288.
  30. Chen, X., 2011, American option pricing formula for uncertain financial market, International Journal of Operations Research, Vol. 8, No. 2, pp., 32-37.
  31. Liu, B., 2013, Toward uncertain finance theory, Journal of Uncertainty Analysis and Applications, Vol. 1, No. 1, pp., 1-15.
  32. Peng, Z. X., 2012, Complex uncertain variable, Doctoral Dissertation, Tsinghua University.
  33. You, C. L., 2009, On the convergence of uncertain sequences, Mathematical and Computer Modelling, Vol. 49, pp., 482-487.
  34. Zhang, Z., 2011, Some discussions on uncertain measure, Fuzzy Optimization and Decision Making, Vol. 10, No. 1, pp., 31-43.
  35. Guo, H., Xu, C., 2013, A necessary and sufficient condition of convergence in mean square for uncertain sequence, Information: An International Interdisciplinary Journal, Vol. 16, No. 2(A), pp.,1091-1096.
  36. Tripathy, B. C., Nath, P. K., 2017, Statistical Convergence of Complex Uncertain Sequences, New Mathematics and Natural Computation, Vol. 13, No. 3), pp., 359-374.
  37. Kişi, Ö., Ünal H. K., Lacunary Statistical Convergence of Complex Uncertain Sequence, International Conference on Applied Analysis and Mathematical Modelling (ICAAMM2019), Istanbul, Turkey.
  38. Kişi, Ö., I-Lacunary Statistical Convergence of Complex Uncertain Sequence, under review.