Vijay Gupta, Cristina Radu (2009)
Open Mathematics
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In the present paper we introduce a q-analogue of the Baskakov-Kantorovich operators and investigate their weighted statistical approximation properties. By using a weighted modulus of smoothness, we give some direct estimations for error in case 0 < q < 1.
Nazim Mahmudov, Havva Kaffaoğlu (2010)
Open Mathematics
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In the present paper, we introduce the q-Szász-Durrmeyer operators and justify a local approximation result for continuous functions in terms of moduli of continuity. We also discuss a Voronovskaya type result for the q-Szász-Durrmeyer operators.
Mei-Ying Ren, Xiao-Ming Zeng (2013)
Czechoslovak Mathematical Journal
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Very recently the -Bernstein-Schurer operators which reproduce only constant function were introduced and studied by C. V. Muraru (2011). Inspired by J. P. King, Positive linear operators which preserve (2003), in this paper we modify -Bernstein-Schurer operators to King type modification of -Bernstein-Schurer operators, so that these operators reproduce constant as well as quadratic test functions and study the approximation properties of these operators. We establish a convergence...
Sharma, Honey (2009)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Nazim Mahmudov (2010)
Open Mathematics
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In the present paper we introduce and investigate weighted statistical approximation properties of a q-analogue of the Baskakov and Baskakov-Kantorovich operators. By using a weighted modulus of smoothness, we give some direct estimations for error in the case 0 < q < 1.
Aral, Ali, Doğru, Ogün (2007)
Journal of Inequalities and Applications [electronic only]
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Verdoodt, Ann (1994)
Bulletin of the Belgian Mathematical Society - Simon Stevin
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Heiner Gonska, Radu Păltănea (2010)
Czechoslovak Mathematical Journal
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We introduce and study a one-parameter class of positive linear operators constituting a link between the well-known operators of S. N. Bernstein and their genuine Bernstein-Durrmeyer variants. Several limiting cases are considered including one relating our operators to mappings investigated earlier by Mache and Zhou. A recursion formula for the moments is proved and estimates for simultaneous approximation of derivatives are given.
Gupta, Vijay, Ispir, Nurhayat (2004)
International Journal of Mathematics and Mathematical Sciences
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