We study in this paper a generalization of the notion of a discrete hypergroup with particular emphasis on the relation with systems of orthogonal polynomials. The concept of a locally compact hypergroup was introduced by Dunkl [8], Jewett [12] and Spector [25]. It generalizes convolution algebras of measures associated to groups as well as linearization formulae of classical families of orthog...

The purpose of this paper is to define a new equivalence relation τ∗ on divisible hypergroups and to show that this relation is the smallest strongly regular relation (the fundamental relation) on commutative divisible hypergroups. We show that τ∗ ̸= β∗, τ∗ ̸= γ∗ and, we define a divisible hypergroup on every nonempty set. We show that the quotient of a finite divisible hypergroup by τ∗ is the tr...

Maji et al. introduced the concept of fuzzy soft sets as a generalization of the standard soft sets and presented an application of fuzzy soft sets in a decision making problem. The aim of this paper is to apply the concept of fuzzy soft sets to n-ary hypergroup theory. The concepts of (∈(γ), ∈(γ) ∨ q(δ))-fuzzy soft (invertible) n-ary subhypergroups over a commutative n-ary hypergroup are intro...

The concept of a locally compact hypergroup was introduced by Dunkl [6], Jewett [14] and Spector [26]. Hypergroups generalize convolution algebras of measures associated to groups as well as linearization formulae of classical families of special functions, e.g. orthogonal polynomials. Many results of harmonic analysis on locally compact abelian groups can be carried over to the case of commuta...

The objective of this paper is to introduce the concept of neutrosophic hypergroup and present some of its elementary properties.

In this paper using strongly duplexes we introduce a new class of (semi)hypergroups. The associated (semi)hypergroup from a strongly duplex is called duplex (semi)hypergroup. Two computer programs written in MATLAB show that the two groups $Z_{2n}$ and $Z_{n}times Z_{2}$ produce a strongly duplex and its associated hypergroup is a complementary feasible hypergroup.

An algebraic quantum group is a regular multiplier Hopf algebra with integrals. In this paper we will develop a theory of algebraic quantum hypergroups. It is very similar to the theory of algebraic quantum groups, except that the comultiplication is no longer assumed to be a homomorphism. We still require the existence of a left and of a right integral. There is also an antipode but it is char...

in this paper using strongly duplexes we introduce a new class of (semi)hypergroups. the associated (semi)hypergroup from a strongly duplex is called duplex (semi)hypergroup. two computer programs written in matlab show that the two groups $z_{2n}$ and $z_{n}times z_{2}$ produce a strongly duplex and its associated hypergroup is a complementary feasible hypergroup.