Applications of Bernstein-Durrmeyer operators in estimating the covering number

The paper deals with estimates of the covering number for some Mercer kernel Hilbert space with Bernstein-Durrmeyer operators. We first give estimates of l ² — norm of Mercer kernel matrices reproducing by the kernels

$K^{left( {alpha ,beta } right)} left( {x,y} right): = sumlimits_{k = 0}^infty {C_k ^{left( {alpha ,beta } right)} Q_k ^{left( {alpha ,beta } right)} left( x right)Q_k ^{left( {alpha ,beta } right)} left( y right)} $K^{left( {alpha ,beta } right)} left( {x,y} right): = sumlimits_{k = 0}^infty {C_k ^{left( {alpha ,beta } right)} Q_k ^{left( {alpha ,beta } right)} left( x right)Q_k ^{left( {alpha ,beta } right)} left( y right)}
Keywords:	Mercer kernel matrix  covering number  Bernstein-Durrmeyer operator
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