scholarly journals Approximation by complex modified Szász-Mirakjan-Stancu operators in compact disks

Filomat ◽  
2015 ◽  
Vol 29 (5) ◽  
pp. 1007-1019 ◽  
Author(s):  
Nursel Çetin
Keyword(s):  
Rate Of Convergence ◽  
Exponential Growth ◽  
Analytic Functions ◽  
Exact Order ◽  
Order Of Approximation ◽  
Stancu Operators ◽  
Exact Order Of Approximation ◽  
Compact Disks

In this paper, we establish some theorems on approximation and Voronovskaja type results for complex modified Sz?sz-Mirakjan-Stancu operators attached to analytic functions having exponential growth on compact disks. Also, we estimate the rate of convergence and the exact order of approximation.

scholarly journals Approximation by complex Szász-Mirakyan-Stancu-Durrmeyer operators in compact disks under exponential growth

Filomat ◽  
2015 ◽  
Vol 29 (5) ◽  
pp. 1127-1136
Author(s):  
Sorin Gal ◽  
Vijay Gupta
Keyword(s):  
Exponential Growth ◽  
Analytic Functions ◽  
Exact Order ◽  
Order Of Approximation ◽  
Durrmeyer Operators ◽  
Exact Order Of Approximation ◽  
Quantitative Estimates ◽  
Compact Disks

In the present paper, we deal with the complex Sz?sz-Stancu-Durrmeyer operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth on compact disks. Also, the exact order of approximation is found.

Voronovskaja’s theorem, shape preserving properties and iterations for complex q-Bernstein polynomials

2011 ◽  
Vol 48 (1) ◽  
pp. 23-43 ◽  
Author(s):  
Sorin Gal
Keyword(s):  
Convergence Theorem ◽  
Analytic Functions ◽  
Quantitative Estimate ◽  
Bernstein Polynomials ◽  
Exact Order ◽  
Approximation Properties ◽  
Shape Preserving ◽  
Voronovskaja’S Theorem ◽  
Shape Preserving Properties ◽  
Compact Disks

In this paper, first we prove Voronovskaja’s convergence theorem for complex q-Bernstein polynomials, 0 < q < 1, attached to analytic functions in compact disks in ℂ centered at origin, with quantitative estimate of this convergence. As an application, we obtain the exact order in approximation of analytic functions by the complex q-Bernstein polynomials on compact disks. Finally, we study the approximation properties of their iterates for any q > 0 and we prove that the complex qn-Bernstein polynomials with 0 < qn < 1 and qn → 1, preserve in the unit disk (beginning with an index) the starlikeness, convexity and spiral-likeness.

Approximation by complex Chlodowsky-Szasz-Durrmeyer operators in compact disks

2020 ◽  
Vol 29 (1) ◽  
pp. 37-44
Author(s):  
AYDIN IZGI ◽  
SEVILAY KIRCI SERENBAY
Keyword(s):  
Error Estimates ◽  
Exponential Growth ◽  
Analytic Functions ◽  
Approximation Properties ◽  
Type Result ◽  
Durrmeyer Operators ◽  
Numerical Example ◽  
Compact Disks

This paper presents a study on the approximation properties of the operators constructed by the composition of Chlodowsky operators and Szasz-Durrmeyer operators. We give the approximation properties and obtain a Voronovskaya-type result for these operators for analytic functions of exponential growth on compact disks. Furthermore, a numerical example with an illustrative graphic is given to compare for the error estimates of the operators.

Blending type approximation by complex Szász-Durrmeyer-Chlodowsky operators in compact disks

2019 ◽  
Vol 69 (5) ◽  
pp. 1077-1088
Author(s):  
Meenu Goyal ◽  
P. N. Agrawal
Keyword(s):  
Analytic Functions ◽  
Simultaneous Approximation ◽  
Asymptotic Result ◽  
Exact Order ◽  
Approximation Properties ◽  
Type Result ◽  
Type Approximation ◽  
Quantitative Estimates ◽  
Compact Disks ◽  
Upper Estimate

Abstract In the present article, we deal with the overconvergence of the Szász-Durrmeyer-Chlodowsky operators. Here we study the approximation properties e.g. upper estimates, Voronovskaja type result for these operators attached to analytic functions in compact disks. Also, we discuss the exact order in simultaneous approximation by these operators and its derivatives and the asymptotic result with quantitative upper estimate. In such a way, we put in evidence the overconvergence phenomenon for the Szász-Durrmeyer-Chlodowsky operators, namely the extensions of approximation properties with exact quantitative estimates and orders of these convergencies to sets in the complex plane that contain the interval [0, ∞).

On Global Inverse Theorems of Szász and Baskakov Operators

1979 ◽  
Vol 31 (2) ◽  
pp. 255-263 ◽  
Author(s):  
Z. Ditzian
Keyword(s):  
Rate Of Convergence ◽  
Exponential Growth ◽  
Polynomial Growth ◽  
Continuous Functions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Baskakov Operators ◽  
Inverse Theorems ◽  
Image Position ◽  
Necessary And Sufficient

The Szász and Baskakov approximation operators are given by1.11.2respectively. For continuous functions on [0, ∞) with exponential growth (i.e. ‖ƒ‖A ≡ supx\ƒ(x)e–Ax\ < M) the modulus of continuity is defined by1.3where ƒ ∈ Lip* (∝, A) for some 0 < ∝ ≦ 2 if w2(ƒ, δ, A) ≦ Mδ∝ for all δ < 1. We shall find a necessary and sufficient condition on the rate of convergence of An(ƒ, x) (representing Sn(ƒ, x) or Vn(ƒ, x)) to ƒ(x) for ƒ(x) ∈ Lip* (∝, A). In a recent paper of M. Becker [1] such conditions were found for functions of polynomial growth (where (1 + \x\N)−1 replaced e–Ax in the above). M. Becker explained the difficulties in treating functions of exponential growth.

Sign in / Sign up

Export Citation Format

Share Document