Double Integral Operators Concerning Starlike of Order

Double integral operators which were considered by S. S. Miller and P. T. Mocanu (Integral Transform. Spec. Funct. 19(2008), 591–597) are discussed. In order to show the analytic function () is starlike of order in the open unit disk , the theory of differential subordinations for analytic functions is applied. The object of the present paper is to discuss some interesting conditions for () to be starlike of order in concerned with second-order differential inequalities and double integral operators.