scholarly journals Convergence properties of Ibragimov-Gadjiev-Durrmeyer operators

2015 ◽  
Vol 24 (1) ◽  
pp. 17-26
Author(s):  
EMRE DENIZ ◽  
◽  
ALI ARAL ◽  
Keyword(s):  
Weighted Space ◽  
Type Theorem ◽  
Approximation Error ◽  
Weighted Norm ◽  
Approximation Properties ◽  
Convergence Properties ◽  
Korovkin Type Theorem ◽  
Durrmeyer Operators ◽  
Weighted Modulus ◽  
Direct Approximation

The purpose of the present paper is to study the local and global direct approximation properties of the Durrmeyer type generalization of Ibragimov Gadjiev operators defined in [Aral, A. and Acar, T., On Approximation Properties of Generalized Durrmeyer Operators, (submitted)]. The results obtained in this study consist of Korovkin type theorem which enables us to approximate a function uniformly by new Durrmeyer operators, and estimate for approximation error of the operators in terms of weighted modulus of continuity. These results are obtained for the functions which belong to weighted space with polynomial weighted norm by new operators which act on functions defined on the non compact interval [0.∞). We finally present a direct approximation result.

scholarly journals Approximation Properties of Ibragimov-Gadjiev-Durrmeyer Operators on Lp (ℝ+)

2017 ◽  
Vol 50 (1) ◽  
pp. 156-174
Author(s):  
Gülsüm Ulusoy ◽  
Ali Aral
Keyword(s):  
Type Theorem ◽  
Modulus Of Smoothness ◽  
Weighted Norm ◽  
Approximation Properties ◽  
Korovkin Type Theorem ◽  
Approximation Process ◽  
Durrmeyer Operators ◽  
New Class ◽  
Positive Approximation Process ◽  
Durrmeyer Type Operators

Abstract We deal with the approximation properties of a new class of positive linear Durrmeyer type operators which offer a reconstruction of integral type operators including well known Durrmeyer operators. This reconstruction allows us to investigate approximation properties of the Durrmeyer operators at the same time. It is first shown that these operators are a positive approximation process in Lp(ℝ+) . While we are showing this property of the operators we consider the Ditzian-Totik modulus of smoothness and corresponding K-functional. Then, weighted norm convergence, whose proof is based on Korovkin type theorem on Lp(ℝ+), is given. At the end of the paper we show several examples of classical sequences that can be obtained from the Ibragimov-Gadjiev-Durrmeyer operators.

Approximation by Stancu–Chlodowsky type λ-Bernstein operators

2020 ◽  
Vol 26 (1) ◽  
pp. 97-110
Author(s):  
M. Mursaleen ◽  
A. A. H. Al-Abied ◽  
M. A. Salman
Keyword(s):  
Asymptotic Formula ◽  
Weighted Space ◽  
Direct Result ◽  
Bernstein Operators ◽  
Approximation Properties ◽  
Convergence Properties ◽  
Korovkin’S Theorem

AbstractIn this paper, we give some approximation properties by Stancu–Chlodowsky type λ-Bernstein operators in the polynomial weighted space and obtain the convergence properties of these operators by using Korovkin’s theorem. We also establish the direct result and the Voronovskaja type asymptotic formula.

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 modified Srivastava-Gupta operators based on certain parameter

2018 ◽  
Vol 38 (1) ◽  
pp. 41-53 ◽  
Author(s):  
Alok Kumar ◽  
Dr Vandana
Keyword(s):  
Maximal Function ◽  
Statistical Convergence ◽  
Approximation Theorem ◽  
Type Theorem ◽  
Weighted Approximation ◽  
Linear Functions ◽  
Approximation Properties ◽  
Voronovskaja Type Theorem ◽  
Direct Approximation ◽  
Lipschitz Type Maximal Function

In the present article, we give a modified form of generalized Srivastava-Gupta operators based on certain parameter which preserve the constant as well as linear functions. First, we estimate moments of the operators and then prove Voronovskaja type theorem. Next, direct approximation theorem, rate of convergence and weighted approximation by these operators in terms of modulus of continuity are studied. Then, we obtain point-wise estimate using the Lipschitz type maximal function. Finaly, we study the $A$-statistical convergence of these operators.

scholarly journals Approximation by generalized Stancu type integral operators involving Sheffer polynomials

2018 ◽  
Vol 34 (2) ◽  
pp. 215-228
Author(s):  
M. MURSALEEN ◽  
◽  
SHAGUFTA RAHMAN ◽  
KHURSHEED J. ANSARI ◽  
◽  
...  
Keyword(s):  
Modulus Of Continuity ◽  
Integral Operators ◽  
Modulus Of Smoothness ◽  
Approximation Properties ◽  
Convergence Properties ◽  
Weighted Modulus Of Continuity ◽  
Type Integral ◽  
Weighted Modulus ◽  
Sheffer Polynomials ◽  
Korovkin’S Theorem

In this article, we give a generalization of integral operators which involves Sheffer polynomials introduced by Sucu and Buy¨ ukyazici. We obtain approximation properties of our operators with the help of the univer- ¨ sal Korovkin’s theorem and study convergence properties by using modulus of continuity, the second order modulus of smoothness and Peetre’s K-functional. We have also established Voronovskaja type asymptotic formula. Furthermore, we study the convergence of these operators in weighted spaces of functions on the positive semi-axis and estimate the approximation by using 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.

Korovkin-type theorems and applications

2009 ◽  
Vol 7 (2) ◽  
Author(s):  
Nazim Mahmudov
Keyword(s):  
Type Theorem ◽  
Linear Operators ◽  
Bernstein Operator ◽  
Approximation Properties ◽  
Korovkin Type Theorem ◽  
Quantitative Results ◽  
Korovkin Type Theorems

AbstractLet {T n} be a sequence of linear operators on C[0,1], satisfying that {T n (e i)} converge in C[0,1] (not necessarily to e i) for i = 0,1,2, where e i = t i. We prove Korovkin-type theorem and give quantitative results on C 2[0,1] and C[0,1] for such sequences. Furthermore, we define King’s type q-Bernstein operator and give quantitative results for the approximation properties of such operators.

scholarly journals APPROXIMATION PROPERTIES OF MODIFIED BASKAKOV GAMMA OPERATORS

2021 ◽  
pp. 125
Author(s):  
Seda Arpagus ◽  
Ali Olgun
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Type Theorem ◽  
Weighted Spaces ◽  
Approximation Properties ◽  
Korovkin Type Theorem ◽  
Gamma Operator ◽  
Voronovskaya Type Theorem

In this present paper, we study an approximation properties of modified Baskakov-Gamma operator. Using Korovkin type theorem we first give approximation properties of this operator. Secondly, we compute the rate of convergence of this operator by means of the modulus of continuity and we give an approximation properties of weighted spaces. Finally, we study the Voronovskaya type theorem of this operator.

scholarly journals Approximation by generalized integral Favard-Szász type operators involving Sheffer polynomials

Filomat ◽  
2019 ◽  
Vol 33 (7) ◽  
pp. 1921-1935
Author(s):  
Seda Karateke ◽  
Çiğdem Atakut ◽  
İbrahim Büyükyazıcı
Keyword(s):  
Modulus Of Continuity ◽  
Order Of Convergence ◽  
Type Theorem ◽  
Type Operator ◽  
Weighted Spaces ◽  
Approximation Properties ◽  
Integral Type ◽  
Korovkin Type Theorem ◽  
Numerical Examples ◽  
Sheffer Polynomials

This article deals with the approximation properties of a generalization of an integral type operator in the sense of Favard-Sz?sz type operators including Sheffer polynomials with graphics plotted using Maple. We investigate the order of convergence, in terms of the first and the second order modulus of continuity, Peetre?s K-functional and give theorems on convergence in weighted spaces of functions by means of weighted Korovkin type theorem. At the end of the work, we give some numerical examples.

scholarly journals New integral type operators

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2851-2865
Author(s):  
Emre Deniz ◽  
Ali Aral ◽  
Gulsum Ulusoy
Keyword(s):  
Pointwise Convergence ◽  
Weighted Space ◽  
Approximation Theorem ◽  
Modulus Of Smoothness ◽  
Integral Type ◽  
Type Estimate ◽  
Lp Space ◽  
Weighted Modulus ◽  
Direct Approximation ◽  
Kantorovich Operators

In this paper we construct new integral type operators including heritable properties of Baskakov Durrmeyer and Baskakov Kantorovich operators. Results concerning convergence of these operators in weighted space and the hypergeometric form of the operators are shown. Voronovskaya type estimate of the pointwise convergence along with its quantitative version based on the weighted modulus of smoothness are given. Moreover, we give a direct approximation theorem for the operators in suitable weighted Lp space on [0,?).

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