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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.
Mahmudov, N.I., Sabancıgil, P. (2008)
Journal of Inequalities and Applications [electronic only]
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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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Aral, Ali, Doğru, Ogün (2007)
Journal of Inequalities and Applications [electronic only]
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Zoltán Finta, Vijay Gupta (2010)
Open Mathematics
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We establish direct estimates for the q-Baskakov operator introduced by Aral and Gupta in [2], using the second order Ditzian-Totik modulus of smoothness. Furthermore, we define and study the limit q-Baskakov operator.
Abdul Wafi, Salma Khatoon (2008)
Open Mathematics
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In the present paper our aim is to establish convergence and Voronovskaja-type theorems for first derivatives of generalized Baskakov operators for functions of one and two variables in exponential and polynomial weight spaces.
Octavian Agratini, Ioan A. Rus (2003)
Commentationes Mathematicae Universitatis Carolinae
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In this paper we are concerned with a general class of positive linear operators of discrete type. Based on the results of the weakly Picard operators theory our aim is to study the convergence of the iterates of the defined operators and some approximation properties of our class as well. Some special cases in connection with binomial type operators are also revealed.