The growth and approximation for an analytic function represented by Laplace-Stieltjes transforms with generalized order converging in the half plane.

Abstract

By utilizing the concept of generalized order, we investigate the growth of Laplace-Stieltjes transform converging in the half plane and obtain one equivalence theorem concerning the generalized order of Laplace-Stieltjes transforms. Besides, we also study the problem on the approximation of this Laplace-Stieltjes transform and give some results about the generalized order, the error, and the coefficients of Laplace-Stieltjes transforms. Our results are extension and improvement of the previous theorems given by Luo and Kong, Singhal, and Srivastava.