King type modification of q-Bernstein-Schurer operators |
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Authors: | Mei-Ying Ren Xiao-Ming Zeng |
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Affiliation: | 1. Department of Mathematics and Computer Science, Wuyi University, Wuyishan, 354 300, P.R.China 2. Department of Mathematics, Xiamen University, Xiamen, 361 005, P.R.China
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Abstract: | Very recently the q-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 x 2 (2003), in this paper we modify q-Bernstein-Schurer operators to King type modification of q-Bernstein-Schurer operators, so that these operators reproduce constant as well as quadratic test functions x 2 and study the approximation properties of these operators. We establish a convergence theorem of Korovkin type. We also get some estimations for the rate of convergence of these operators by using modulus of continuity. Furthermore, we give a Voronovskaja-type asymptotic formula for these operators. |
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