El Bab, A. S. OkbGhany, Hossam. A.2020-01-142020-01-142010Cited References in Web of Science Core Collection: 9978-0-7354-0863-0https://ijpam.eu/contents/2010-64-1/2/2.pdfAccession Number: WOS:000287125700035The main task in this article is to give the necessary and sufficient conditions guarantees that the product of two positive definite functions defined on a hypergroup X is also positive definite on X. Also, we prove that a continuous function with compact support psi is negative definite if and only if exp(-t psi) is positive definite for each t > 0. Moreover, we will give some relations between the class of completely monotonic functions on a hypergroup and the set of tau- positive functions.enUniversity for HypergroupPositive definiteCompletely monotoneBook chapter