scholarly journals Approximation properties of (p;q)-variant of Stancu-Schurer operators

2018 ◽  
Vol 37 (4) ◽  
pp. 137-151 ◽  
Author(s):  
Abdul Wafi ◽  
Nadeem Rao ◽  
_ Deepmala
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Continuous Functions ◽  
Second Order ◽  
Lipschitz Class ◽  
Approximation Properties ◽  
Direct Approximation ◽  
Korovkin Type Theorems

In this article, we have introduced (p;q)-variant of Stancu-Schurer operators and discussed the rate of convergence for continuous functions. We have also discussed recursive estimates, Korovkin-type theorems and direct approximation results using second order modulus of continuity, Peetre’s K-functional and Lipschitz class.

The Dunkl generalization of Stancu type q-Szasz-Mirakjan-Kantorovich operators and some approximation results

2018 ◽  
Vol 34 (3) ◽  
pp. 363-370
Author(s):  
M. MURSALEEN ◽  
◽  
MOHD. AHASAN ◽  
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Exponential Function ◽  
Second Order ◽  
Lipschitz Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Approximation Properties ◽  
Kantorovich Operators ◽  
Korovkin’S Theorem

In this paper, a Dunkl type generalization of Stancu type q-Szasz-Mirakjan-Kantorovich positive linear operators ´ of the exponential function is introduced. With the help of well-known Korovkin’s theorem, some approximation properties and also the rate of convergence for these operators in terms of the classical and second-order modulus of continuity, Peetre’s K-functional and Lipschitz functions are investigated.

scholarly journals Summation-Integral Type Operators Based on Lupas-Jain Functions

2021 ◽  
Vol 45 (02) ◽  
pp. 309-322
Author(s):  
NESIBE MANAV ◽  
NURHAYAT ISPIR
Keyword(s):  
Modulus Of Continuity ◽  
Local Approximation ◽  
Degree Of Approximation ◽  
Continuous Functions ◽  
Lipschitz Class ◽  
Approximation Properties ◽  
Integral Type ◽  
Base Functions

We introduce a genuine summation-integral type operators based on Lupaş-Jain type base functions related to the unbounded sequences. We investigated their degree of approximation in terms of modulus of continuity and ????-functional for the functions from bounded and continuous functions space. Furthermore, we give some theorems for the local approximation properties of functions belonging to Lipschitz class. Also, we give Voronovskaja theorem for these operators.

scholarly journals Some approximation results for (p,q)-Lupaş-Schurer operators

Filomat ◽  
2018 ◽  
Vol 32 (1) ◽  
pp. 217-229 ◽  
Author(s):  
K. Kanat ◽  
M. Sofyalıoğlu
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Approximation Theorem ◽  
Lipschitz Class ◽  
Approximation Properties ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation

In this paper, we introduce Lupa?-Schurer operators based on (p,q)-integers. Then, we deal with the approximation properties for (p,q)-Lupa?-Schurer operators based on Korovkin type approximation theorem. Moreover, we compute rate of convergence by using modulus of continuity, with the help of functions of Lipschitz class and Peetre?s K-functionals.

q -Laguerre type linear positive operators

2007 ◽  
Vol 44 (1) ◽  
pp. 65-80 ◽  
Author(s):  
Mehmet Özarslan
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Positive Operators ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Lipschitz Class ◽  
Approximation Properties ◽  
Linear Positive Operators ◽  
The Difference

The main object of this paper is to define the q -Laguerre type positive linear operators and investigate the approximation properties of these operators. The rate of convegence of these operators are studied by using the modulus of continuity, Peetre’s K -functional and Lipschitz class functional. The estimation to the difference | Mn +1, q ( ƒ ; χ )− Mn , q ( ƒ ; χ )| is also obtained for the Meyer-König and Zeller operators based on the q -integers [2]. Finally, the r -th order generalization of the q -Laguerre type operators are defined and their approximation properties and the rate of convergence of this r -th order generalization are also examined.

scholarly journals Kantrovich Type Generalization of Meyer-Konig and Zeller Operators via Generating Functions

2013 ◽  
Vol 21 (3) ◽  
pp. 209-222 ◽  
Author(s):  
Ali Olgun ◽  
H. Gül İnce ◽  
Fatma Tasdelen
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Generating Functions ◽  
Type Theorem ◽  
Lipschitz Class ◽  
Approximation Properties ◽  
Korovkin Type Theorem

Abstract In the present paper, we study a Kantorovich type generalization of Meyer-König and Zeller type operators via generating functions. Using Korovkin type theorem we first give approximation properties of these operators defined on the space C [0;A] ; 0 < A < 1. Secondly, we compute the rate of convergence of these operators by means of the modulus of continuity and the elements of the modified Lipschitz class. Finally, we give an r-th order generalization of these operators in the sense of Kirov and Popova and we obtain approximation properties of them.

scholarly journals On the rates of convergence of the q-Lupaş-Stancu operators

Filomat ◽  
2016 ◽  
Vol 30 (5) ◽  
pp. 1151-1160
Author(s):  
Ogün Doğru ◽  
Gürhan İçoz ◽  
Kadir Kanat
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Rates Of Convergence ◽  
Lipschitz Class ◽  
Approximation Properties ◽  
Statistical Approximation ◽  
Stancu Operators

We introduce a Stancu type generalization of the Lupa? operators based on the q-integers, rate of convergence of this modification are obtained by means of the modulus of continuity, Lipschitz class functions and Peetre?s K-functional. We will also introduce r-th order generalization of these operators and obtain its statistical approximation properties.

scholarly journals General family of exponential operators

Filomat ◽  
2020 ◽  
Vol 34 (12) ◽  
pp. 4043-4060
Author(s):  
Km. Lipi ◽  
Naokant Deo
Keyword(s):  
Rate Of Convergence ◽  
Error Estimation ◽  
Bounded Variation ◽  
Approximation Theorem ◽  
Modulus Of Smoothness ◽  
Lipschitz Class ◽  
Approximation Properties ◽  
Approximation Of Functions ◽  
Direct Approximation ◽  
Derivatives Of

In this article, we deal with the approximation properties of Ismail-May operators [16] based on a non-negative real parameter ?. We provide some graphs and error estimation table for a numerical example depicting the convergence of our proposed operators. We further define the B?zier variant of these operators and give a direct approximation theorem using Ditizan-Totik modulus of smoothness and a Voronovoskaya type asymptotic theorem. We also study the error in approximation of functions having derivatives of bounded variation. Lastly, we introduce the bivariate generalization of Ismail May operators and estimate its rate of convergence for functions of Lipschitz class.

scholarly journals The Rate of Convergence of Lupasq-Analogue of the Bernstein Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Heping Wang ◽  
Yanbo Zhang
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Continuous Functions ◽  
Bernstein Operators ◽  
Lipschitz Continuous Functions ◽  
Lipschitz Continuous

We discuss the rate of convergence of the Lupasq-analogues of the Bernstein operatorsRn,q(f;x)which were given by Lupas in 1987. We obtain the estimates for the rate of convergence ofRn,q(f)by the modulus of continuity off, and show that the estimates are sharp in the sense of order for Lipschitz continuous functions.

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.

scholarly journals Moduli of continuity, functional spaces,\break and elliptic boundary value problems. The full regularity spaces Cα0,λ(Ω̅)

2018 ◽  
Vol 7 (1) ◽  
pp. 15-34 ◽  
Author(s):  
Hugo Beirão da Veiga
Keyword(s):  
Modulus Of Continuity ◽  
Elliptic Boundary ◽  
Continuous Functions ◽  
Second Order ◽  
Hölder Spaces ◽  
Elliptic Boundary Value ◽  
New Class ◽  
Holder Spaces ◽  
Derivatives Of ◽  
Full Regularity

AbstractLet {\boldsymbol{L}} be a second order uniformly elliptic operator, and consider the equation {\boldsymbol{L}u=f} under the boundary condition {u=0}. We assume data f in generical subspaces of continuous functions {D_{\overline{\omega}}} characterized by a given modulus of continuity{\overline{\omega}(r)}, and show that the second order derivatives of the solution u belong to functional spaces {D_{\widehat{\omega}}}, characterized by a modulus of continuity{\widehat{\omega}(r)} expressed in terms of {\overline{\omega}(r)}. Results are optimal. In some cases, as for Hölder spaces, {D_{\widehat{\omega}}=D_{\overline{\omega}}}. In this case we say that full regularity occurs. In particular, full regularity occurs for the new class of functional spaces {C^{0,\lambda}_{\alpha}(\overline{\Omega})} which includes, as a particular case, the classical Hölder spaces {C^{0,\lambda}(\overline{\Omega})=C^{0,\lambda}_{0}(\overline{\Omega})}. Few words, concerning the possibility of generalizations and applications to non-linear problems, are expended at the end of the introduction and also in the last section.

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