The estimation of the operational functions of the type exp

Abstract

J. Mikusiński presented in the paper [2] the estimation of the operational function e-*’\ ote(0,l), in some unbounded set of R + x R 1. The results obtained by J. Mikusiński were generalized in the paper [3]. The similar estimation of the function exp y bs'A x is made in the above paper, where P^eR and p^eCO.l), v = 1....n. This paper is devoted to the investigation of the behaviour more general operational functions, when the coefficients /?„ are in C and fulfilling some relations concerning their real and imaginary parts.