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Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 69 Issue: 1

Generalized difference sequence spaces of fractional order defined by Orlicz functions

Nazlım Deniz Aral(BITLIS EREN UNIVERSITY)0000-0002-8984-2620
Mikail Et(FIRAT UNIVERSITY)0000-0001-8292-7819
Sayfa
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Yayın Tarihi
2020-06-30
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

We establish some connections between Δ^{α}-lacunary strongly convergence of order β and Δ^{α}-lacunary statistical convergence of order β.

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Amaç & Hipotez:The main purpose of this paper is to introduce the concepts of Δ^{α}-lacunary statistical convergence of order β (0<β≤1) with the fractional order of α and Δ^{α}-lacunary strongly convergence of order β (0<β≤1) with the fractional order of α.
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Temel Bulgular & Veri:The main purpose of this paper is to introduce the concepts of Δ^{α}-lacunary statistical convergence of order β (0<β≤1) with the fractional order of α and Δ^{α}-lacunary strongly convergence of order β (0<β≤1) with the fractional order of α.
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Sonuç & Katkı:We establish some connections between Δ^{α}-lacunary strongly convergence of order β and Δ^{α}-lacunary statistical convergence of order β.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Difference sequence · Statistical convergence · Lacunary sequence

Abstract

The main purpose of this paper is to introduce the concepts of Δ^{α}-lacunary statistical convergence of order β (0<β≤1) with the fractional order of α and Δ^{α}-lacunary strongly convergence of order β (0<β≤1) with the fractional order of α. We establish some connections between Δ^{α}-lacunary strongly convergence of order β and Δ^{α}-lacunary statistical convergence of order β.

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Bu Makaleye Atıf Yap

Aral, N. D., Et, M. (2020). Generalized difference sequence spaces of fractional order defined by Orlicz functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 69 Issue: 1. https://doi.org/10.31801/cfsuasmas.628863

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Kaynakça (47)

  1. Altınok, H., Et, M., Çolak, R., Some remarks on generalized sequence space of bounded variation of sequences of fuzzy numbers, Iran. J. Fuzzy Syst., 11(5) (2014), 39--46, 109.
  2. Aral, N. D., Et, M., On lacunary statistical convergence of order β of difference sequences of fractional order, International Conference of Mathematical Sciences, (ICMS 2019), Maltepe University, Istanbul, Turkey.
  3. Baliarsingh, P., Some new difference sequence spaces of fractional order and their dual spaces, Appl. Math. Comput., 219(18) (2013), 9737--9742.
  4. Baliarsingh, P., Kadak, U., Mursaleen, M., On statistical convergence of difference sequences of fractional order and related Korovkin type approximation theorems, Quaest. Math., 41(8) (2018), 1117--1133.
  5. Belen, C., Mohiuddine, S. A., Generalized weighted statistical convergence and application, Appl. Math. Comput., 219 (2013), 9821-9826.
  6. Bhardwaj, V. K., Singh, N., Some sequences defined by Orlicz functions, Demonstratio Math., 33(3) (2000), 571-582.
  7. Çakallı, H., Lacunary statistical convergence in topological groups, Indian J. Pure Appl. Math., 26(2) (1995), 113--119.
  8. Çakallı, H., Aras, C. G., Sönmez, A., Lacunary statistical ward continuity, AIP Conf. Proc., 1676, 020042 (2015); http://dx.doi.org/10.1063/1.4930468.
  9. Çakallı, H., Kaplan, H., A variation on lacunary statistical quasi Cauchy sequences, Commun. Fac. Sci. Univ. Ank. Sér. A1 Math. Stat., 66(2) (2017), 71--79.
  10. Caserta, A., Di Maio, G., Kočinac, L. D. R., Statistical convergence in function spaces, Abstr. Appl. Anal., 2011, Art. ID 420419, 11 pp.
  11. Çınar, M., Karakaş, M., Et, M., On pointwise and uniform statistical convergence of order α for sequences of functions, Fixed Point Theory And Applications, Article Number: 33, 2013.
  12. Çolak, R., Statistical convergence of order α, Modern Methods in Analysis and Its Applications, New Delhi, India: Anamaya Pub., (2010) 121--129.
  13. Connor, J. S., The statistical and strong p-Cesaro convergence of sequences, Analysis, 8 (1988), 47-63.
  14. Et, M., Çolak, R., On some generalized difference sequence spaces, Soochow J. Math., 21(4) (1995), 377-386.
  15. Et, M., Tripathy, B. C., Dutta, A. J., On pointwise statistical convergence of order α of sequences of fuzzy mappings, Kuwait J. Sci., 41(3) (2014), 17--30.
  16. Et, M., Mursaleen, M., Işık, M., On a class of fuzzy sets defined by Orlicz functions, Filomat, 27(5) (2013), 789--796.
  17. Et, M., Çolak, R., Altin, Y., Strongly almost summable sequences of order α, Kuwait J. Sci., 41(2) (2014), 35--47.
  18. Et, M., Nuray, F., Δ^{m}-Statistical convergence, Indian J. Pure appl. Math. 32(6) (2001), 961 - 969.
  19. Et, M., Şengül, H., Some Cesaro-Type Summability Spaces of Order alpha and Lacunary Statistical Convergence of Order α, Filomat, 28(8) (2014), 1593-1602.
  20. Fast, H., Sur la convergence statistique, Colloq. Math., 2 (1951), 241-244.
  21. Freedman, A. R., Sember, J. J., Raphael, M., Some Cesaro-type summability spaces, Proc. Lond. Math. Soc., 37(3) (1978), 508-520.
  22. Fridy, J., On statistical convergence, Analysis, 5 (1985), 301-313.
  23. Fridy, J., Orhan, C., Lacunary statistical convergence, Pacific J. Math., 160 (1993), 43-51.
  24. Kadak, U., Generalized lacunary statistical difference sequence spaces of fractional order, Int. J. Math. Math. Sci., 2015, Art. ID 984283, 6 pp.
  25. Kadak, U., Mohiuddine, S. A., Generalized statistically almost convergence based on the difference operator which includes the (p, q)-gamma function and related approximation theorems, Results Math., 73(1) (2018), Article 9.
  26. Karakaş, M., Et, M., Karakaya, V., Some geometric properties of a new difference sequence space involving lacunary sequences, Acta Math. Sci. Ser. B (Engl. Ed.), 33(6) (2013), 1711--1720.
  27. Kızmaz, H., On certain sequence spaces, Canad. Math. Bull., 24(2) (1981), 169-176.
  28. Krasnosel'skii, M. A.,Rutickii, Y. B., Convex Functions and Orlicz Spaces, Groningen, Netherlands, (1961).
  29. Lindberg, K., On subspaces of Orlicz sequence spaces, Studia Math., 45 (1973), 119-146.
  30. Lindenstrauss, J., Tzafriri, T., On Orlicz sequence spaces, Israel J. Math., 10 (1971), 379-390.
  31. Mohiuddine, S. A., Alamri, B. A. S., Generalization of equi-statistical convergence via weighted lacunary sequence with associated Korovkin and Voronovskaya type approximation theorems, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM, 113(3) (2019), 1955-1973.
  32. Mohiuddine, S. A., Asiri, A., Hazarika, B., Weighted statistical convergence through difference operator of sequences of fuzzy numbers with application to fuzzy approximation theorems, Int. J. Gen. Syst., 48(5) (2019), 492-506.
  33. Mursaleen, M., λ- statistical convergence, Math. Slovaca, 50(1) (2012), 111 -115.
  34. Mursaleen, M., Khan, Q. A., Chishti, T. A., Some new convergent sequences spaces defined by Orlicz functions and statistical convergence, Ital. J. Pure Appl. Math., 9 (2001), 25-32.
  35. Nayak, L., Et, M., Baliarsingh, P., On certain generalized weighted mean fractional difference sequence spaces, Proc. Nat. Acad. Sci. India Sect. A, 89(1) (2019), 163--170.
  36. Savaş, E., Et, M., On (Δ_{λ}^{m},I)-statistical convergence of order α, Period. Math. Hungar., 71(2) (2015), 135--145.
  37. Savaş, E., Rhoades, B. E., On some new sequence spaces of invariant means defined by Orlicz functions, Math. Inequal. Appl., 5(2) (2002), 271-281.
  38. Schoenberg, I. J., The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66 (1959), 361-375.
  39. Şengül, H., Et, M., On lacunary statistical convergence of order α, Acta Mathematica Scientia, 34(2) 473-482.
  40. Srivastava, H. M., Et, M., Lacunary statistical convergence and strongly lacunary summable functions of order α, Filomat, 31(6) (2017), 1573--1582.
  41. Salat, T., On statistically convergent sequences of real numbers, Math. Slovaca, 30 (1980), 139-150.
  42. Steinhaus, H., Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math., 2 (1951), 73--74.
  43. Tripathy, B. C., Hazarika, B., Some I-convergent sequence spaces defined by Orlicz functions, Acta Math. Appl. Sin. Engl. ser., 27(1) (2011), 149-154.
  44. Tripathy, B. C., Et, M., On generalized difference lacunary statistical convergence, Studia Univ. Babeş-Bolyai Math., 50(1) (2005), 119--130.
  45. Zygmund, A., Trigonometric Series, Cambridge University Press, Cambridge, UK, 1979.
  46. Et, M., Çolak, R., On some generalized difference sequence spaces, Soochow J. Math., 21(4) (1995), 377-386.
  47. Et, M., Nuray, F., Δ^{m}-Statistical convergence, Indian J. Pure appl. Math. 32(6) (2001), 961 - 969.