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q-Szász-Mirakyan-Kantorovich type operators preserving some test functions. (English) Zbl 1251.41008
The paper under review concerns the approximation property of q-analogue of the well-known Szász-Mirakyan-Kantorovich operators. The authors introduce a q-analogue of the Szász-Mirakyan-Kantorovich operators and propose two different modifications of these operators using the classical q-analogue of the integration in the interval [0,b] see [F. H. Jackson, Q. J. 41, 193–203 (1910; JFM 41.0317.04)]. These modifications preserve some test functions. They also examine the rate of convergence for the constructed operators by means of modulus of continuity.
41A35Approximation by operators (in particular, by integral operators)
41A25Rate of convergence, degree of approximation
41A36Approximation by positive operators
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