scholarly journals The generalization of certain results for Szasz-Mirakjan-Schurer operators

2012 ◽  
Vol 21 (1) ◽  
pp. 79-85
Author(s):  
DAN MICLAUS ◽  
◽  
OVIDIU T. POP ◽  
Keyword(s):  
Uniform Convergence ◽  
Present Article ◽  
General Formula ◽  
Modulus Of Continuity ◽  
Type Theorem ◽  
Order Of Approximation ◽  
Test Functions ◽  
Voronovskaja Type Theorem

The present article continues earlier research by authors, in order to reach two goals. Firstly, we give a general formula concerning calculation of the test functions by Szasz-Mirakjan-Schurer operators and secondly, we establish a Voronovskaja type theorem, the uniform convergence and the ´ order of approximation using the modulus of continuity for the same operators.

scholarly journals The generalization of some results for Bernstein and Stancu operators

2011 ◽  
Vol 20 (2) ◽  
pp. 147-156
Author(s):  
DAN MICLAUS ◽  
◽  
PETRU I. BRAICA ◽  
Keyword(s):  
Uniform Convergence ◽  
Type Theorem ◽  
Bernstein Operators ◽  
Order Of Approximation ◽  
Test Functions ◽  
Stancu Operators ◽  
Voronovskaja Type Theorem

In the present paper we generalize some results for Bernstein and Stancu operators. Firstly, we establish a relationship between two results concerning calculation of test functions by Bernstein operators. Secondly, using this relationship and some known results we prove in every case a Voronovskaja type theorem, the uniform convergence and the order of approximation for Bernstein and Stancu operators.

scholarly journals On Stancu-Type Generalization of Modified p , q -Szász-Mirakjan-Kantorovich Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yong-Mo Hu ◽  
Wen-Tao Cheng ◽  
Chun-Yan Gui ◽  
Wen-Hui Zhang
Keyword(s):  
Rate Of Convergence ◽  
Present Article ◽  
Modulus Of Continuity ◽  
Type Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Pointwise Estimates ◽  
Approximation Properties ◽  
Voronovskaja Type Theorem ◽  
Kantorovich Operators

In the present article, we construct p , q -Szász-Mirakjan-Kantorovich-Stancu operators with three parameters λ , α , β . First, the moments and central moments are estimated. Then, local approximation properties of these operators are established via K -functionals and Steklov mean in means of modulus of continuity. Also, a Voronovskaja-type theorem is presented. Finally, the pointwise estimates, rate of convergence, and weighted approximation of these operators are studied.

scholarly journals Generalized p,q-Gamma-type operators

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Wen-Tao Cheng ◽  
Qing-Bo Cai
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Type Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Pointwise Estimates ◽  
Approximation Properties ◽  
Central Moments ◽  
Voronovskaja Type Theorem

In the present paper, the generalized p,q-gamma-type operators based on p,q-calculus are introduced. The moments and central moments are obtained, and some local approximation properties of these operators are investigated by means of modulus of continuity and Peetre K-functional. Also, the rate of convergence, weighted approximation, and pointwise estimates of these operators are studied. Finally, a Voronovskaja-type theorem is presented.

Modified Lupaş-Jain operators

2020 ◽  
Vol 70 (2) ◽  
pp. 431-440 ◽  
Author(s):  
Murat Bodur
Keyword(s):  
Modulus Of Continuity ◽  
Type Theorem ◽  
Weighted Spaces ◽  
Order Of Approximation ◽  
Weighted Modulus Of Continuity ◽  
Quantitative Form ◽  
Voronovskaya Type Theorem ◽  
Weighted Modulus

Abstract The goal of this paper is to propose a modification of Lupaş-Jain operators based on a function ρ having some properties. Primarily, the convergence of given operators in weighted spaces is discussed. Then, order of approximation via weighted modulus of continuity is computed for these operators. Further, Voronovskaya type theorem in quantitative form is taken into consideration, as well. Ultimately, some graphical results that illustrate the convergence of investigated operators to f are given.

scholarly journals Dunkl generalization of q-Szász-Mirakjan operators which preserve x2

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 733-747 ◽  
Author(s):  
Mohammad Mursaleen ◽  
Shagufta Rahman
Keyword(s):  
Modulus Of Continuity ◽  
Exponential Function ◽  
Type Theorem ◽  
Convergence Properties ◽  
Voronovskaja Type Theorem

In the present paper we construct q-Sz?sz-Mirakjan operators generated by Dunkl generalization of the exponential function which preserve x2. We obtain some approximation results via universal Korovkin?s type theorem for these operators and study convergence properties by using the modulus of continuity. Furthermore, we obtain a Voronovskaja type theorem for these operators.

scholarly journals Stancu-variant of generalized Baskakov operators

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2625-2632 ◽  
Author(s):  
Nadeem Rao ◽  
Abdul Wafi
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Type Theorem ◽  
Modulus Of Smoothness ◽  
Order Of Approximation ◽  
Baskakov Operators ◽  
Direct Estimate ◽  
Voronovskaya Type Theorem

In the present paper, we introduce Stancu-variant of generalized Baskakov operators and study the rate of convergence using modulus of continuity, order of approximation for the derivative of function f . Direct estimate is proved using K-functional and Ditzian-Totik modulus of smoothness. In the last, we have proved Voronovskaya type theorem.

scholarly journals Note on a Schurer-Stancu-type operator

2015 ◽  
Vol 24 (1) ◽  
pp. 61-67
Author(s):  
ADRIAN D. INDREA ◽  
◽  
ANAMARIA INDREA ◽  
PETRU I. BRAICA ◽  
◽  
...  
Keyword(s):  
Type Theorem ◽  
Type Operator ◽  
Test Functions ◽  
New Class ◽  
Voronovskaja Type Theorem

The aim of this paper is to introduce a class of operators of Schurer-Stancu-type with the property that the test functions e0 and e1 are reproduced. Also, in our approach, a theorem of error approximation and a Voronovskaja-type theorem for this operators are obtained. Finally, we study the convergence of the iterates for our new class of operators.

scholarly journals Note On Jakimovski-Leviatan Operators Preserving e–x

2019 ◽  
Vol 4 (2) ◽  
pp. 543-550 ◽  
Author(s):  
Ecem Acar ◽  
Aydın İzgi ◽  
Sevilay Kirci Serenbay
Keyword(s):  
Uniform Convergence ◽  
Present Article ◽  
Quantitative Estimate ◽  
Type Theorem ◽  
Convergence Order

AbstractIn the present article, a modification of Jakimovski-Leviatan operators is presented which reproduce constant and e–x functions. We prove uniform convergence order of a quantitative estimate for the modified operators. We also give a quantitative Voronovskya type theorem.

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.

scholarly journals On bivariate Jain operators

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Münüse Akçay ◽  
Gülen Başcanbaz-Tunca
Keyword(s):  
Modulus Of Continuity ◽  
Type Theorem ◽  
Elementary Method ◽  
Voronovskaja Type Theorem

<p style='text-indent:20px;'>In this paper we deal with bivariate extension of Jain operators. Using elementary method, we show that these opearators are non-increasing in <inline-formula><tex-math id="M1">\begin{document}$ n $\end{document}</tex-math></inline-formula> when the attached function is convex. Moreover, we demonstrate that these operators preserve the properties of modulus of continuity. Finally, we present a Voronovskaja type theorem for the sequence of bivariate Jain operators.</p>

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