The \(h\)-Fourier cosine-Laplace generalized convolution with a weight function

Abstract. We construct \(h\)-Fourier cosine-Laplace discrete generalized convolution with a weight function on time scale \(\mathbb{T}_h^0\) and study its properties. We obtain some inequalities for this generalized convolution such as Young's type inequalities, Saitoh's type inequalities. In the application, we apply this generalized convolution to solve some linear equations of generalized convolution type.

Key words and phrases. \(h\)-Laplace transform, \(h\)-Fourier cosine transform, generalized convolution, generalized convolution inequality.