The paper deals with estimates of the covering number for some Mercer kernel Hilbert space with Bernstein-Durrmeyer operators. We first give estimates of l2-norm of Mercer kernel matrices reproducing by the kernels K(α,β)(x,y) :=sum from k=0 to ∞ (Ck( α,β)Qk(α ,β)(x)Qk(α ,β)(y)), where Qk(α ,β)(x) are the Jacobi polynomials of order k on (0,1),Ck( α,β)> 0 are real numbers, and from which give the lower and upper bounds of the covering number for some particular reproducing kernel Hilbert space reproduced by K(α,β)(x,y).
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