Abstract:

Based on properties of exponentially bounded C-Cosine functions, the Taylor expansion formula for exponentially bounded C-Cosine functions is obtained. By means of Pettis integral, Holder inequality and moment-generating functions of some suitable random variables, the probabilistic approximations and Vonorovskaya type asymptotic formula for C-Cosine functions are given.

Key words: exponentially bounded C-Cosine functions; Taylor expansion formula; probabilistic approximations; Vonorovskaya type asymptotic formula