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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 $\left[0,b\right]$ 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.
##### MSC:
 41A35 Approximation by operators (in particular, by integral operators) 41A25 Rate of convergence, degree of approximation 41A36 Approximation by positive operators