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ρ-STATISTICAL CONVERGENCE DEFINED BY A MODULUS FUNCTION OF ORDER (α,β)

Yıl 2022, Cilt: 4 Sayı: 1, 15 - 23, 30.04.2022

Nazlım Deniz Aral

https://doi.org/10.47087/mjm.1092599
Cited By: 1

Öz

The concept of strong w [ρ, f, q] −summability of order (α, β) for sequences of complex (or real) numbers is introduced in this work. We also give some inclusion relations between the sets of ρ-statistical convergence of order (α, β), strong wαβ [ρ, f, q] −summability and strong wαβ (ρ, q) −summability.

Anahtar Kelimeler

Ces`aro summability modulus function statistical convergence.

Kaynakça

  • Y. Altın, Properties of some sets of sequences defined by a modulus function, Acta Math. Sci. Ser. B Engl. Ed. 29(2) (2009), 427–434.
  • N. D. Aral and H. Sengul Kandemir, I-Lacunary statistical Convergence of order β of difference sequences of fractional order, Facta Universitatis (NIS) Ser. Math. Inform. 36(1) (2021), 43–55.
  • A. Caserta, Di M. Giuseppe and L. D. R. Koˇcinac, Statistical convergence in function spaces, Abstr. Appl. Anal. 2011, Art. ID 420419, 11 pp.
  • J. S. Connor, The Statistical and Strong p-Cesaro Convergence of Sequences, Analysis, 8, pp. (1988), 47-63.
  • H. Cakallı, H. S ̧engu ̈l Kandemir and M. Et, ρ-statistical convergence of order beta, American Institute of Physics., https://doi.org/10.1063/1.5136141.
  • H. Cakallı, A study on statistical convergence, Funct. Anal. Approx. Comput. 1(2) (2009), 19–24.
  • R. Colak, Statistical convergence of order α, Modern Methods in Analysis and Its Applications, New Delhi, India: Anamaya Pub, 2010: 121–129.
  • M. Et, Generalized Ces`aro difference sequence spaces of non-absolute type involving lacunary sequences, Appl. Math. Comput. 219(17) (2013), 9372–9376.
  • M. Et, M. Cınar and H. Sengul, On ∆m−asymptotically deferred statistical equivalent sequences of order α, Filomat, 33(7) (2019), 1999–2007.
  • M. Et and H. Sengul, Some Cesaro-type summability spaces of order α and lacunary statistical convergence of order α, Filomat, 28(8) (2014), 1593–1602.
  • M. Et, Strongly almost summable difference sequences of order m defined by a modulus, Studia Sci. Math. Hungar. 40(4) (2003), 463–476.
  • M. Et, Spaces of Ces`aro difference sequences of order r defined by a modulus function in a locally convex space, Taiwanese J. Math. 10(4) (2006), 865-879.
  • H. Fast, Sur La Convergence Statistique, Colloq. Math., 2, pp. (1951), 241–244.
  • J. Fridy, On Statistical Convergence, Analysis, 5, pp. (1985), 301-313.
  • A. D. Gadjiev and C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain J. Math. 32(1) (2002), 129-138.
  • M. Isık, Strongly almost (w, λ, q)−summable sequences, Math. Slovaca 61(5) (2011), 779– 788.
  • E. Kolk, The statistical convergence in Banach spaces, Acta Comment. Univ. Tartu, 928 (1991), 41-52.
  • I. J. Maddox, Elements of Functional Analysis, Cambridge University Press, 1970.
  • I. J. Maddox, Sequence spaces defined by a modulus, Math. Proc. Camb. Philos. Soc, 1986, 100:161-166.
  • A. K. Gaur and M. Mursaleen, Difference sequence spaces defined by a sequence of moduli, Demonstratio Math. 31(2) (1998), 275–278.
  • H. Nakano, Modulared sequence spaces, Proc. Japan Acad. 27 (1951), 508–512.
  • F. Nuray and E. Savas, Some new sequence spaces defined by a modulus function, Indian J. Pure Appl. Math. 24(11) (1993), 657–663.
  • S. Pehlivan and B. Fisher, Lacunary strong convergence with respect to a sequence of mod- ulus functions, Comment. Math. Univ. Carolin. 36(1) (1995), 69-76.
  • S. Pehlivan and B. Fisher, Some sequence spaces defined by a modulus, Mathematica Slo- vaca, 45(3) (1995), 275–280.
  • W. H. Ruckle, FK spaces in which the sequence of coordinate vectors is bounded, Canad. J. Math. 25 (1973), 973–978.
  • T. Salat, On Statistically Convergent Sequences of Real Numbers, Math. Slovaca. 30 (1980), 139-150.
  • I. J. Schoenberg, The Integrability of Certain Functions and Related Summability Methods, Amer. Math. Monthly 66 (1959), 361–375.
  • H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2 (1951) 73-74.
  • H. Sengul, Some Ces`aro summability spaces defined by a modulus function of order (α,β), Commun. Fac .Sci. Univ. Ank. Series A1 66(2) (2017), 80–90.
  • H. Sengul, On Wijsman I−lacunary statistical equivalence of order (η,μ), J. Inequal. Spec. Funct. 9(2) (2018), 92–101.
  • H. Sengul and M. Et, f−lacunary statistical convergence and strong f−lacunary summability of order α, Filomat 32(13) (2018), 4513–4521.
  • H. Sengul and M. Et, On (λ,I)−statistical convergence of order α of sequences of function, Proc. Nat. Acad. Sci. India Sect. A 88(2) (2018), 181–186.
  • H.Sengul and O. Koyun, On (λ,A)−statistical convergence of order α, Commun.Fac.Sci. Univ. Ank. Ser. A1. Math. Stat. 68(2) (2019), 2094–2103.
  • H. Sengul and M. Et, On lacunary statistical convergence of order α, Acta Math. Sci. Ser. B Engl. Ed. 34(2) (2014), 473–482.

Yıl 2022, Cilt: 4 Sayı: 1, 15 - 23, 30.04.2022

Nazlım Deniz Aral

https://doi.org/10.47087/mjm.1092599
Cited By: 1

Öz

Kaynakça

  • Y. Altın, Properties of some sets of sequences defined by a modulus function, Acta Math. Sci. Ser. B Engl. Ed. 29(2) (2009), 427–434.
  • N. D. Aral and H. Sengul Kandemir, I-Lacunary statistical Convergence of order β of difference sequences of fractional order, Facta Universitatis (NIS) Ser. Math. Inform. 36(1) (2021), 43–55.
  • A. Caserta, Di M. Giuseppe and L. D. R. Koˇcinac, Statistical convergence in function spaces, Abstr. Appl. Anal. 2011, Art. ID 420419, 11 pp.
  • J. S. Connor, The Statistical and Strong p-Cesaro Convergence of Sequences, Analysis, 8, pp. (1988), 47-63.
  • H. Cakallı, H. S ̧engu ̈l Kandemir and M. Et, ρ-statistical convergence of order beta, American Institute of Physics., https://doi.org/10.1063/1.5136141.
  • H. Cakallı, A study on statistical convergence, Funct. Anal. Approx. Comput. 1(2) (2009), 19–24.
  • R. Colak, Statistical convergence of order α, Modern Methods in Analysis and Its Applications, New Delhi, India: Anamaya Pub, 2010: 121–129.
  • M. Et, Generalized Ces`aro difference sequence spaces of non-absolute type involving lacunary sequences, Appl. Math. Comput. 219(17) (2013), 9372–9376.
  • M. Et, M. Cınar and H. Sengul, On ∆m−asymptotically deferred statistical equivalent sequences of order α, Filomat, 33(7) (2019), 1999–2007.
  • M. Et and H. Sengul, Some Cesaro-type summability spaces of order α and lacunary statistical convergence of order α, Filomat, 28(8) (2014), 1593–1602.
  • M. Et, Strongly almost summable difference sequences of order m defined by a modulus, Studia Sci. Math. Hungar. 40(4) (2003), 463–476.
  • M. Et, Spaces of Ces`aro difference sequences of order r defined by a modulus function in a locally convex space, Taiwanese J. Math. 10(4) (2006), 865-879.
  • H. Fast, Sur La Convergence Statistique, Colloq. Math., 2, pp. (1951), 241–244.
  • J. Fridy, On Statistical Convergence, Analysis, 5, pp. (1985), 301-313.
  • A. D. Gadjiev and C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain J. Math. 32(1) (2002), 129-138.
  • M. Isık, Strongly almost (w, λ, q)−summable sequences, Math. Slovaca 61(5) (2011), 779– 788.
  • E. Kolk, The statistical convergence in Banach spaces, Acta Comment. Univ. Tartu, 928 (1991), 41-52.
  • I. J. Maddox, Elements of Functional Analysis, Cambridge University Press, 1970.
  • I. J. Maddox, Sequence spaces defined by a modulus, Math. Proc. Camb. Philos. Soc, 1986, 100:161-166.
  • A. K. Gaur and M. Mursaleen, Difference sequence spaces defined by a sequence of moduli, Demonstratio Math. 31(2) (1998), 275–278.
  • H. Nakano, Modulared sequence spaces, Proc. Japan Acad. 27 (1951), 508–512.
  • F. Nuray and E. Savas, Some new sequence spaces defined by a modulus function, Indian J. Pure Appl. Math. 24(11) (1993), 657–663.
  • S. Pehlivan and B. Fisher, Lacunary strong convergence with respect to a sequence of mod- ulus functions, Comment. Math. Univ. Carolin. 36(1) (1995), 69-76.
  • S. Pehlivan and B. Fisher, Some sequence spaces defined by a modulus, Mathematica Slo- vaca, 45(3) (1995), 275–280.
  • W. H. Ruckle, FK spaces in which the sequence of coordinate vectors is bounded, Canad. J. Math. 25 (1973), 973–978.
  • T. Salat, On Statistically Convergent Sequences of Real Numbers, Math. Slovaca. 30 (1980), 139-150.
  • I. J. Schoenberg, The Integrability of Certain Functions and Related Summability Methods, Amer. Math. Monthly 66 (1959), 361–375.
  • H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math. 2 (1951) 73-74.
  • H. Sengul, Some Ces`aro summability spaces defined by a modulus function of order (α,β), Commun. Fac .Sci. Univ. Ank. Series A1 66(2) (2017), 80–90.
  • H. Sengul, On Wijsman I−lacunary statistical equivalence of order (η,μ), J. Inequal. Spec. Funct. 9(2) (2018), 92–101.
  • H. Sengul and M. Et, f−lacunary statistical convergence and strong f−lacunary summability of order α, Filomat 32(13) (2018), 4513–4521.
  • H. Sengul and M. Et, On (λ,I)−statistical convergence of order α of sequences of function, Proc. Nat. Acad. Sci. India Sect. A 88(2) (2018), 181–186.
  • H.Sengul and O. Koyun, On (λ,A)−statistical convergence of order α, Commun.Fac.Sci. Univ. Ank. Ser. A1. Math. Stat. 68(2) (2019), 2094–2103.
  • H. Sengul and M. Et, On lacunary statistical convergence of order α, Acta Math. Sci. Ser. B Engl. Ed. 34(2) (2014), 473–482.
Toplam 34 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Nazlım Deniz Aral

Yayımlanma Tarihi 30 Nisan 2022
Kabul Tarihi 5 Mayıs 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 4 Sayı: 1

Kaynak Göster

APA Aral, N. D. (2022). ρ-STATISTICAL CONVERGENCE DEFINED BY A MODULUS FUNCTION OF ORDER (α,β). Maltepe Journal of Mathematics, 4(1), 15-23. https://doi.org/10.47087/mjm.1092599
AMA Aral ND. ρ-STATISTICAL CONVERGENCE DEFINED BY A MODULUS FUNCTION OF ORDER (α,β). Maltepe Journal of Mathematics. Nisan 2022;4(1):15-23. doi:10.47087/mjm.1092599
Chicago Aral, Nazlım Deniz. “ρ-STATISTICAL CONVERGENCE DEFINED BY A MODULUS FUNCTION OF ORDER (α,β)”. Maltepe Journal of Mathematics 4, sy. 1 (Nisan 2022): 15-23. https://doi.org/10.47087/mjm.1092599.
EndNote Aral ND (01 Nisan 2022) ρ-STATISTICAL CONVERGENCE DEFINED BY A MODULUS FUNCTION OF ORDER (α,β). Maltepe Journal of Mathematics 4 1 15–23.
IEEE N. D. Aral, “ρ-STATISTICAL CONVERGENCE DEFINED BY A MODULUS FUNCTION OF ORDER (α,β)”, Maltepe Journal of Mathematics, c. 4, sy. 1, ss. 15–23, 2022, doi: 10.47087/mjm.1092599.
ISNAD Aral, Nazlım Deniz. “ρ-STATISTICAL CONVERGENCE DEFINED BY A MODULUS FUNCTION OF ORDER (α,β)”. Maltepe Journal of Mathematics 4/1 (Nisan 2022), 15-23. https://doi.org/10.47087/mjm.1092599.
JAMA Aral ND. ρ-STATISTICAL CONVERGENCE DEFINED BY A MODULUS FUNCTION OF ORDER (α,β). Maltepe Journal of Mathematics. 2022;4:15–23.
MLA Aral, Nazlım Deniz. “ρ-STATISTICAL CONVERGENCE DEFINED BY A MODULUS FUNCTION OF ORDER (α,β)”. Maltepe Journal of Mathematics, c. 4, sy. 1, 2022, ss. 15-23, doi:10.47087/mjm.1092599.
Vancouver Aral ND. ρ-STATISTICAL CONVERGENCE DEFINED BY A MODULUS FUNCTION OF ORDER (α,β). Maltepe Journal of Mathematics. 2022;4(1):15-23.

Cited By

ON ρ-STATISTICAL CONVERGENCE OF ORDER (α,β) FOR SEQUENCES OF FUZZY NUMBERS
Middle East Journal of Science
https://doi.org/10.51477/mejs.1326338
 Kapak Resmi İndir

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