Grüss and Grüss-Voronovskaya-type estimates for complex convolution polynomial operators

Sorın GAL; Ionut T. IANCU

doi:https://doi.org/10.33205/cma.780906

Makale detayları

Grüss and Grüss-Voronovskaya-type estimates for complex convolution polynomial operators

Yazarlar:

Sorın GAL | Ionut T. IANCU

Yayıncı:

Tuncer ACAR

Ana Başlıklar:

Matematik

Dergi:

Constructive Mathematical Analysis 2021 Vol.4 Issue 1, pp.20-33

Belge Tipi:

Makale

Yayın Tarihi:

2/2021

Belge Dili:

İngilizce

Document ID (Org No.):

2000914154

Sıklık:

Üç Aylık

pISSN:

2651-2939

DOI:

https://doi.org/10.33205/cma.780906

Özet:

 

A classical well-known result in approximation theory is the  Grüss inequality for positive linear functionals, which  gives an upper bound for the Chebyshev-type functional.

Starting also from a problem posed by Gavrea, this inequality was also investigated in terms of the least concave majorants of the moduli of continuity and for positive linear operators by Acu, Gonska, Rasa and Rusu, where the cases of classical Hermite-Fejer and Fejer-Korovkin convolution operators were considered.

Refined versions of the Grüss-type inequality in the spirit of Voronovskaya's theorem were obtained by Gal and Gonska
for Bernstein and Paltanea operators of real variable and for complex Bernstein, genuine Bernstein-Durrmeyer and Bernstein-Faber operators attached to analytic functions of complex variable.

After the appearance of these papers, several papers by other authors have developed these directions of research.

The goal of this paper is to continue the above mentioned directions of research, obtaining Grüss and Grüss-Voronovskaya exact estimates (with respect to the degree of polynomials) for the de la Vallee-Poussin complex polynomials in Section 2, for Zygmund-Riesz complex polynomials in Section 3 and for Jackson complex polynomials in Section 4.

Makale detayları

Grüss and Grüss-Voronovskaya-type estimates for complex convolution polynomial operators

Yazarlar: Sorın GAL | Ionut T. IANCU

Yayıncı: Tuncer ACAR

Ana Başlıklar: Matematik

Dergi: Constructive Mathematical Analysis 2021 Vol.4 Issue 1, pp.20-33

Belge Tipi: Makale

Yayın Tarihi: 2/2021

Belge Dili: İngilizce

Document ID (Org No.): 2000914154

Sıklık: Üç Aylık

pISSN: 2651-2939

DOI: https://doi.org/10.33205/cma.780906

Sayı

Yazarlar:

Sorın GAL | Ionut T. IANCU

Yayıncı:

Tuncer ACAR

Ana Başlıklar:

Matematik

Dergi:

Constructive Mathematical Analysis 2021 Vol.4 Issue 1, pp.20-33

Belge Tipi:

Makale

Yayın Tarihi:

2/2021

Belge Dili:

İngilizce

Document ID (Org No.):

2000914154

Sıklık:

Üç Aylık

pISSN:

2651-2939

DOI:

https://doi.org/10.33205/cma.780906