Applications of the Bernstein-Durrmeyer operators in estimating the norm of Mercer kernel matrices

The paper is related to the norm estimate of Mercer kernel matrices. The lower and upper bound estimates of Rayleigh entropy numbers for some Mercer kernel matrices on [0,1]×[0,1] based on the Bernstein-Durrmeyer operator kernel are obtained, with which and the approximation property of the Bernstein-Durrmeyer operator the lower and upper bounds of the Rayleigh entropy number and the l2—norm for general Mercer kernel matrices on [0,1]×[0,1] are provided.