Convolution inequalities of the Fourier cosine transform and the Laplace with a weight function

Abstract

In this paper, we research generalized convolution inequalities related to the Fourier cosine transform and the Laplace transform with a weight function, the factorization equality contains two different integral transforms. Establish the factorization equalitys, Parseval type equalitys and convolution standard evaluation of the Fourier cosine transforms and Laplace  with a weight function, used in evaluating solutions of differential - integral equations in solving problems information handling.