Some improvements of numerical radius inequalities of operators and operator matrices

We obtain upper bounds for the numerical radius of a product of Hilbert space operators which improve on the existing upper bounds. We generalize the numerical radius inequalities of n× n operator matrices by using non-negative continuous functions on [0,∞). We also obtain some upper and lower bounds for the B-numerical radius of operator matrices, where B is the diagonal operator matrix whose each diagonal entry is a positive operator $A.$ We show that these bounds generalize and improve on the existing bounds.