This paper is concerned with actions of finite hypergroups on sets. After introducing the definitions in the first section, we use the notion of ‘maximal actions’ to characterise those hypergroups which arise from association schemes, introduce the natural sub-class of *-actions of a hypergroup and introduce a geometric condition for the existence of *-actions of a Hermitian hypergroup. Followi...

Let G be a locally compact hypergroup and let K sub-hypergroup of G. (G, K) is Gelfand pair if Mc(G//K), the algebra measures with support on double coset G//K, commutative for convolution. In this paper, assuming that pair, we define study Fourier transform then establish Plancherel theorem K).

Wildberger gave a method to construct a finite hermitian discrete hypergroup from a random walk on a certain kind of finite graphs. In this article, we reveal that his method is applicable to a random walk on a certain kind of infinite graphs. Moreover, we make some observations of finite or infinite graphs on which a random walk produces a hermitian discrete hypergroup.

this paper continues the study of the connection between hyper- groups and fuzzy sets, investigating the length of the sequence of join spaces associated with a hypergroup. the classes of complete hypergroups and of 1-hypergroups are considered and analyzed in this context. finally, we give a method to construct a nite hypergroup with the strong fuzzy grade equal to a given natural number

This paper attempts an exposition of the connection between symmetric spaces and hypergroup theory. This connection is not new to those involved in hypergroups, as the classical symmetric spaces have always provided a very rich source of examples for the theory. However for those working in symmetric spaces, the usefulness of the hypergroup point of view may not be well known. It provides a new...

This paper is written in the framework of Special Issue Mathematics entitled “Hypercompositional Algebra and Applications”, focuses on presentation essential principles hypergroup, which prominent structure hypercompositional algebra. In beginning, it reveals structural relation between two fundamental entities abstract algebra, group hypergroup. Next, presents several types hypergroups, derive...

Wildberger's construction enables us to obtain a hypergroup from random walk on special graph. We will give probability theoretic interpretation products the hypergroup. The can be identified with commutative algebra whose basis is transition matrices. estimate operator norm of such matrix and clarify relationship between their walks.