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Binomial Operator as a Hausdorff Operator of the Euler Type

Yıl 2020, , 165 - 177, 01.12.2020
https://doi.org/10.33205/cma.783993

Öz

In this paper, we prove that the binomial operator is a Hausdorff operator of the Euler
type and consequently, the binomial matrix domain associated with this operator is nothing
new except an Euler sequence space. Therefore, all the results of published papers on the
binomial sequence spaces like [4] can be extracted easily from [1] and the relation between
the binomial and Euler operators that we introduce. Moreover, we compute the norm and
the lower bound of the binomial operator on some sequence spaces.

Kaynakça

  • G. Bennett: Factorizing the classical inequalities. Mem. Amer. Math. Soc. 576 (1996).
  • G. Bennett: Lower bounds for matrices II. Canad. Jour. Math. 44 (1992), 54-74.
  • M. Bisgin: The binomial sequence spaces which include the spaces $\ell_p$ and $\ell_\infty$ and geometric spaces. J. Inequal. Appl. 2016:304 (2016).
  • M. Bisgin: The binomial sequence spaces of nonabsolute type. J. Inequal. Appl. 2016:309 (2016).
  • H. B. Ellidokuzoglu, S. Demiriz and A. Koseoglu: On the paranormed binomial sequence spaces. Universal Journal of Mathematics and Applications 1 (3) (2018), 137-147.
  • D. Foroutannia, H. Roopaei: The norms and the lower bounds for matrix operators on weighted difference sequence spaces. U.P.B. Sci. Bull., Series A, 79 (2) (2017), 151-160.
  • D. Foroutannia, H. Roopaei: Bounds for the norm of lower triangular matrices on the Cesàro weighted sequence space. J. Inequal. Appl. 67 (2017), 1-11.
  • G. H. Hardy: Divergent series. Oxford University press, 1973.
  • G. H. Hardy, J. E. Littlewood \rm and G. Polya: Inequalities, 2nd edition. Cambridge University press, Cambridge, 2001.
  • H. Kizmaz: On certain sequence spaces I. Canad. Math. Bull. 25 (2) (1981), 169-176.
  • J. Meng, M. Song: Binomial difference sequence spaces of order $m$, Advances in difference equations. 2017 241.
  • M. Mursaleen, F. Basar and B. Altay: On the Euler sequence spaces which include the spaces $\ell_p$ and $\ell_\infty$ II. Nonlinear Analysis 65 (2006), 707-717.
  • R. Paltanea: On Geometric Series of Positive Linear Operators. Constr. Math. Anal. 2 (2) (2019), 49-56.
  • H. Roopaei: Norms of summability and Hausdorff mean matrices on difference sequence spaces. Math Ineqal Appl 22 (3) (2019), 983-987.
  • H. Roopaei: Bounds of Hilbert operator on sequence spaces. Concr. Oper. (2020), 155-165.
  • H. Roopaei: Norm of Hilbert operator on sequence spaces. J. Inequal. Appl. 2020:117 (2020).
  • H. Roopaei: A study on Copson operator and its associated sequence space. J. Inequal. Appl. 2020:120 (2020).
  • H. Roopaei: A study on Copson operator and its associated sequence space II. J. Inequal. Appl. 2020:239 (2020).
  • H. Roopaei, F. Ba\csar: On the spaces of Ces\`aro absolutely p-summable, null and convergent sequences. Math. Method Appl. Sci. (2020), 1- 16. H. Roopaei, D. Foroutannia, M. İlkhan \rm and E. E. Kara: Ces\`aro spaces and norm of operators on these matrix domains. Mediterr. J. Math. 17, 121 (2020).
  • H. Roopaei, D. Foroutannia: The norms of certain matrix operators from $ \ell_p$ spaces into $\ell_p(\Delta^n)$ spaces. Linear Multilinear Algebra 67 (4) (2019), 767-776.
  • H. Roopaei, D. Foroutannia: The norm of matrix operators on Ces\`aro weighted sequence space. Linear Multilinear Algebra 67 (1) (2019), 175-185.
  • A. Sönmez: Some new sequence spaces derived by The composition of binomial matrix and double band matrix. Journal of Applied Analysis and Computation 9 (1) (2019), 231-244. T. Yaying, B. Hazarika: On sequence spaces generated by binomial difference operator of fractional order. Mathematica Slovaca 69 (4) (2019).
Yıl 2020, , 165 - 177, 01.12.2020
https://doi.org/10.33205/cma.783993

Öz

Kaynakça

  • G. Bennett: Factorizing the classical inequalities. Mem. Amer. Math. Soc. 576 (1996).
  • G. Bennett: Lower bounds for matrices II. Canad. Jour. Math. 44 (1992), 54-74.
  • M. Bisgin: The binomial sequence spaces which include the spaces $\ell_p$ and $\ell_\infty$ and geometric spaces. J. Inequal. Appl. 2016:304 (2016).
  • M. Bisgin: The binomial sequence spaces of nonabsolute type. J. Inequal. Appl. 2016:309 (2016).
  • H. B. Ellidokuzoglu, S. Demiriz and A. Koseoglu: On the paranormed binomial sequence spaces. Universal Journal of Mathematics and Applications 1 (3) (2018), 137-147.
  • D. Foroutannia, H. Roopaei: The norms and the lower bounds for matrix operators on weighted difference sequence spaces. U.P.B. Sci. Bull., Series A, 79 (2) (2017), 151-160.
  • D. Foroutannia, H. Roopaei: Bounds for the norm of lower triangular matrices on the Cesàro weighted sequence space. J. Inequal. Appl. 67 (2017), 1-11.
  • G. H. Hardy: Divergent series. Oxford University press, 1973.
  • G. H. Hardy, J. E. Littlewood \rm and G. Polya: Inequalities, 2nd edition. Cambridge University press, Cambridge, 2001.
  • H. Kizmaz: On certain sequence spaces I. Canad. Math. Bull. 25 (2) (1981), 169-176.
  • J. Meng, M. Song: Binomial difference sequence spaces of order $m$, Advances in difference equations. 2017 241.
  • M. Mursaleen, F. Basar and B. Altay: On the Euler sequence spaces which include the spaces $\ell_p$ and $\ell_\infty$ II. Nonlinear Analysis 65 (2006), 707-717.
  • R. Paltanea: On Geometric Series of Positive Linear Operators. Constr. Math. Anal. 2 (2) (2019), 49-56.
  • H. Roopaei: Norms of summability and Hausdorff mean matrices on difference sequence spaces. Math Ineqal Appl 22 (3) (2019), 983-987.
  • H. Roopaei: Bounds of Hilbert operator on sequence spaces. Concr. Oper. (2020), 155-165.
  • H. Roopaei: Norm of Hilbert operator on sequence spaces. J. Inequal. Appl. 2020:117 (2020).
  • H. Roopaei: A study on Copson operator and its associated sequence space. J. Inequal. Appl. 2020:120 (2020).
  • H. Roopaei: A study on Copson operator and its associated sequence space II. J. Inequal. Appl. 2020:239 (2020).
  • H. Roopaei, F. Ba\csar: On the spaces of Ces\`aro absolutely p-summable, null and convergent sequences. Math. Method Appl. Sci. (2020), 1- 16. H. Roopaei, D. Foroutannia, M. İlkhan \rm and E. E. Kara: Ces\`aro spaces and norm of operators on these matrix domains. Mediterr. J. Math. 17, 121 (2020).
  • H. Roopaei, D. Foroutannia: The norms of certain matrix operators from $ \ell_p$ spaces into $\ell_p(\Delta^n)$ spaces. Linear Multilinear Algebra 67 (4) (2019), 767-776.
  • H. Roopaei, D. Foroutannia: The norm of matrix operators on Ces\`aro weighted sequence space. Linear Multilinear Algebra 67 (1) (2019), 175-185.
  • A. Sönmez: Some new sequence spaces derived by The composition of binomial matrix and double band matrix. Journal of Applied Analysis and Computation 9 (1) (2019), 231-244. T. Yaying, B. Hazarika: On sequence spaces generated by binomial difference operator of fractional order. Mathematica Slovaca 69 (4) (2019).
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Hadi Roopaei 0000-0001-7190-3387

Yayımlanma Tarihi 1 Aralık 2020
Yayımlandığı Sayı Yıl 2020

Kaynak Göster

APA Roopaei, H. (2020). Binomial Operator as a Hausdorff Operator of the Euler Type. Constructive Mathematical Analysis, 3(4), 165-177. https://doi.org/10.33205/cma.783993
AMA Roopaei H. Binomial Operator as a Hausdorff Operator of the Euler Type. CMA. Aralık 2020;3(4):165-177. doi:10.33205/cma.783993
Chicago Roopaei, Hadi. “Binomial Operator As a Hausdorff Operator of the Euler Type”. Constructive Mathematical Analysis 3, sy. 4 (Aralık 2020): 165-77. https://doi.org/10.33205/cma.783993.
EndNote Roopaei H (01 Aralık 2020) Binomial Operator as a Hausdorff Operator of the Euler Type. Constructive Mathematical Analysis 3 4 165–177.
IEEE H. Roopaei, “Binomial Operator as a Hausdorff Operator of the Euler Type”, CMA, c. 3, sy. 4, ss. 165–177, 2020, doi: 10.33205/cma.783993.
ISNAD Roopaei, Hadi. “Binomial Operator As a Hausdorff Operator of the Euler Type”. Constructive Mathematical Analysis 3/4 (Aralık 2020), 165-177. https://doi.org/10.33205/cma.783993.
JAMA Roopaei H. Binomial Operator as a Hausdorff Operator of the Euler Type. CMA. 2020;3:165–177.
MLA Roopaei, Hadi. “Binomial Operator As a Hausdorff Operator of the Euler Type”. Constructive Mathematical Analysis, c. 3, sy. 4, 2020, ss. 165-77, doi:10.33205/cma.783993.
Vancouver Roopaei H. Binomial Operator as a Hausdorff Operator of the Euler Type. CMA. 2020;3(4):165-77.