scholarly journals Approximation by Genuineq-Bernstein-Durrmeyer Polynomials in Compact Disks in the Caseq>1

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Nazim I. Mahmudov
Keyword(s):  
Open Problem ◽  
Analytic Functions ◽  
Type Theorem ◽  
Linear Operators ◽  
Explicit Formulas ◽  
Rate Of Approximation ◽  
Voronovskaja Type Theorem ◽  
Quantitative Estimates ◽  
Compact Disks ◽  
Durrmeyer Polynomials

This paper deals with approximating properties of the newly definedq-generalization of the genuine Bernstein-Durrmeyer polynomials in the caseq>1, which are no longer positive linear operators onC0,1. Quantitative estimates of the convergence, the Voronovskaja-type theorem, and saturation of convergence for complex genuineq-Bernstein-Durrmeyer polynomials attached to analytic functions in compact disks are given. In particular, it is proved that, for functions analytic inz∈ℂ:z<R,R>q, the rate of approximation by the genuineq-Bernstein-Durrmeyer polynomialsq>1is of orderq−nversus1/nfor the classical genuine Bernstein-Durrmeyer polynomials. We give explicit formulas of Voronovskaja type for the genuineq-Bernstein-Durrmeyer forq>1. This paper represents an answer to the open problem initiated by Gal in (2013, page 115).

Approximation by complex summation-integral type operator in compact disks

2013 ◽  
Vol 63 (5) ◽  
Author(s):  
Vijay Gupta ◽  
Rani Yadav
Keyword(s):  
Complex Plane ◽  
Analytic Functions ◽  
Quantitative Estimate ◽  
Type Operator ◽  
Approximation Properties ◽  
Integral Type ◽  
Quantitative Estimates ◽  
Compact Disks ◽  
Durrmeyer Polynomials

AbstractIn the present paper we estimate a Voronovskaja type quantitative estimate for a certain type of complex Durrmeyer polynomials, which is different from those studied previously in the literature. Such estimation is in terms of analytic functions in the compact disks. In this way, we present the evidence of overconvergence phenomenon for this type of Durrmeyer polynomials, namely the extensions of approximation properties (with quantitative estimates) from real intervals to compact disks in the complex plane. In the end, we mention certain applications.

scholarly journals The Approximation of Bivariate Blending Variant Szász Operators Based Brenke Type Polynomials

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Behar Baxhaku ◽  
Ramadan Zejnullahu ◽  
Artan Berisha
Keyword(s):  
Modulus Of Continuity ◽  
Weighted Space ◽  
Type Theorem ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Weighted Modulus Of Continuity ◽  
Rate Of Approximation ◽  
Szász Operators ◽  
Weighted Modulus

We have constructed a new sequence of positive linear operators with two variables by using Szasz-Kantorovich-Chlodowsky operators and Brenke polynomials. We give some inequalities for the operators by means of partial and full modulus of continuity and obtain a Lipschitz type theorem. Furthermore, we study the convergence of Szasz-Kantorovich-Chlodowsky-Brenke operators in weighted space of function with two variables and estimate the rate of approximation in terms of the weighted modulus of continuity.

scholarly journals Approximation properties of mixed sampling-Kantorovich operators

2020 ◽  
Vol 115 (1) ◽  
Author(s):  
Laura Angeloni ◽  
Danilo Costarelli ◽  
Gianluca Vinti
Keyword(s):  
Uniform Convergence ◽  
Type Theorem ◽  
Approximation Properties ◽  
Convergence Properties ◽  
Voronovskaja Type Theorem ◽  
Quantitative Estimates ◽  
Kantorovich Operators

Abstract In the present paper we study the pointwise and uniform convergence properties of a family of multidimensional sampling Kantorovich type operators. Moreover, besides convergence, quantitative estimates and a Voronovskaja type theorem have been established.

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, ∞).

scholarly journals Rate of Approximation for Modified Lupaş-Jain-Beta Operators

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
M. Qasim ◽  
Asif Khan ◽  
Zaheer Abbas ◽  
Princess Raina ◽  
Qing-Bo Cai
Keyword(s):  
Pointwise Convergence ◽  
Type Theorem ◽  
Local Approximation ◽  
Basis Functions ◽  
Weighted Spaces ◽  
Rate Of Approximation ◽  
Quantitative Estimates ◽  
Voronovskaya Type Theorem ◽  
New Construction

The main intent of this paper is to innovate a new construction of modified Lupaş-Jain operators with weights of some Beta basis functions whose construction depends on σ such that σ0=0 and infx∈0,∞σ′x≥1. Primarily, for the sequence of operators, the convergence is discussed for functions belong to weighted spaces. Further, to prove pointwise convergence Voronovskaya type theorem is taken into consideration. Finally, quantitative estimates for the local approximation are discussed.

scholarly journals About Some Linear Operators

2007 ◽  
Vol 2007 ◽  
pp. 1-13
Author(s):  
Ovidiu T. Pop
Keyword(s):  
Rate Of Convergence ◽  
General Class ◽  
Type Theorem ◽  
Modulus Of Smoothness ◽  
Positive Operators ◽  
Linear Operators ◽  
Linear Positive Operators ◽  
Voronovskaja Type Theorem

Using the method of Jakimovski and Leviatan from their work in 1969, we construct a general class of linear positive operators. We study the convergence, the evaluation for the rate of convergence in terms of the first modulus of smoothness and we give a Voronovskaja-type theorem for these operators.

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.

scholarly journals Stancu type generalization of Szász-Durrmeyer operators involving Brenke-type polynomials

Filomat ◽  
2019 ◽  
Vol 33 (3) ◽  
pp. 855-868
Author(s):  
Rabia Aktaş ◽  
Dilek Söylemez ◽  
Fatma Taşdelen
Keyword(s):  
Hermite Polynomials ◽  
Type Theorem ◽  
Integral Operators ◽  
Rates Of Convergence ◽  
Linear Operators ◽  
Convergence Properties ◽  
Durrmeyer Operators ◽  
Voronovskaja Type Theorem ◽  
Type Integral ◽  
Second Modulus Of Continuity

In the present paper, we introduce a Stancu type generalization of Sz?sz- Durrmeyer operators including Brenke type polynomials. We give convergence properties of these operators via Korovkin?s theorem and the order of convergence by using a classical approach. As an example, we consider a Stancu type generalization of the Durrmeyer type integral operators including Hermite polynomials of variance v. Then, we obtain the rates of convergence by using the second modulus of continuity. Also, for these operators including Hermite polynomials of variance v, we present a Voronovskaja type theorem and r-th order generalization of these positive linear operators.

Majorization of starlike and convex functions of complex order involving linear operators

2016 ◽  
Vol 66 (1) ◽  
Author(s):  
G. Murugusundaramoorthy ◽  
K. Thilagavathi
Keyword(s):  
Linear Operator ◽  
Convex Functions ◽  
Analytic Functions ◽  
Linear Operators ◽  
Starlike And Convex Functions ◽  
Complex Order

AbstractThe main object of this present paper is to investigate the problem of majorization of certain class of analytic functions of complex order defined by the Dziok-Raina linear operator. Moreover we point out some new or known consequences of our main result.

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