Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/de-gruyter/quantitative-q-voronovskaya-and-q-gr-ss-voronovskaya-type-results-for-mSmQQMttv7
References (25)
-
M. Schlosser (2006)
Multilateral Inversion of Ar, Cr, and Dr Basic Hypergeometric SeriesAnnals of Combinatorics, 13
-
A. Aral, T. Acar (2016)
On Approximation Properties of Generalized Durrmeyer Operators -
T. Acar, A. Aral (2015)
On Pointwise Convergence of q-Bernstein Operators and Their q-DerivativesNumerical Functional Analysis and Optimization, 36
-
A. Acu, H. Gonska, I. Raşa (2011)
Grüss-type and Ostrowski-type inequalities in approximation theoryUkrainian Mathematical Journal, 63
-
H. Gonska, R. Păltănea (2010)
General Voronovskaya and Asymptotic Theorems in Simultaneous ApproximationMediterranean Journal of Mathematics, 7
-
H. Gonska, I. Raşa (2008)
Remarks on Voronovskaya's theorem -
T. Acar (2015)
Asymptotic Formulas for Generalized Szász-Mirakyan OperatorsAppl. Math. Comput., 263
-
N. Ispir (2001)
On Modified Baskakov Operators on Weighted SpacesTurkish Journal of Mathematics, 25
-
S. Gal, H. Gonska (2014)
Gr\"uss and Gr\"uss-Voronovskaya-type estimates for some Bernstein-type polynomials of real and complex variablesarXiv: Classical Analysis and ODEs
-
(2006)
On Peano’s form of the Taylor remainder -
(1985)
Linear Positive Operators of Finite Rank (in Russian) -
G. Phillips (2000)
A generalization of the Bernstein polynomials based on the q-integersThe ANZIAM Journal, 42
-
Bernstein polynomials based on the q-integers
Ann. Numer. Math., 4
-
Gülsüm Ulusoy, T. Acar (2016)
q‐Voronovskaya type theorems for q‐Baskakov operatorsMathematical Methods in the Applied Sciences, 39
-
T. Acar, A. Aral, I. Raşa (2016)
The new forms of Voronovskaya’s theorem in weighted spacesPositivity, 20
-
(1987)
A q-analogue of the Bernstein operator -
P. Rajkovic, M. Stankovic, S. Marinkovic (2002)
Mean Value Theorems in q-calculusMatematički Vesnik, 54
-
J. Tariboon, S. Ntouyas (2014)
Quantum integral inequalities on finite intervalsJournal of Inequalities and Applications, 2014
-
(2011)
Tachev, Grüss-type inequalities for positive linear operators with second order moduli,Mat -
N. Mahmudov (2010)
On q-Parametric Szász-Mirakjan OperatorsMediterranean Journal of Mathematics, 7
-
A. Aral (2008)
A generalization of Szász-Mirakyan operators based on q-integersMath. Comput. Model., 47
-
N. Mahmudov (2011)
q-Szász-Mirakjan operators which preserve x2J. Comput. Appl. Math., 235
-
T. Acar, Gülsüm Ulusoy (2016)
Approximation by modified Szász-Durrmeyer operatorsPeriodica Mathematica Hungarica, 72
-
A. Aral, Vijay Gupta (2006)
The q-derivative and applications to q-Szász Mirakyan operatorsCALCOLO, 43
-
V. Videnskii (2005)
On Some Classes of q-parametric Positive linear Operators
- Publisher
- de Gruyter
- Copyright
- Copyright © 2016 by the
- ISSN
- 1072-947X
- eISSN
- 1572-9176
- DOI
- 10.1515/gmj-2016-0007
- Publisher site
- See Article on Publisher Site
Abstract
Abstract In the present paper, we mainly study quantitative Voronovskaya-type theorems for q -Szász operators defined in ( 20 ). We consider weighted spaces of functions and the corresponding weighted modulus of continuity. We obtain the quantitative q -Voronovskaya-type theorem and the q -Grüss–Voronovskaya-type theorem in terms of the weighted modulus of continuity of q -derivatives of the approximated function. In this way, we either obtain the rate of pointwise convergence of q -Szász operators or we present these results for a subspace of continuous functions, although the classical ones are valid for differentiable functions.
Journal
Georgian Mathematical Journal – de Gruyter
Published: Dec 1, 2016