On entire functions of slow growth represented by Dirichlet series
We define a new kind of Durrmeyer-type summation-integral operators and study a global direct theorem for these operators in terms of the Ditzian-Totik modulus of smoothness.
Let f(z), , be analytic in the finite disc |z| < R. The growth properties of f(z) are studied using the mean values and the iterated mean values of f(z). A convexity result for the above mean values is obtained and their relative growth is studied using the order and type of f(z).
In the present paper, we study the polynomial approximation of entire functions of several complex variables. The characterizations of generalized order and generalized type of entire functions of slow growth have been obtained in terms of approximation and interpolation errors.
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