in this paper the class of n-ary hypergroups is introduced and several properties are found andexamples are presented. n-ary hypergroups are a generalization of hypergroups in the sense of marty. on theother hand, we can consider n-ary hypergroups as a good generalization of n-ary groups. we define thefundamental relation β* on an n-ary hypergroup h as the smallest equivalence relation such tha...

In this paper, we introduce a new class of (semi)hypergroup from a given (partially) quasi-ordered (semi)hypergroup as a generalization of {it "$El$--hyperstructures"}. Then, we study some basic properties and important elements belong to this class.}

Let (Rn(x))n∈N0 be an orthogonal sequence inducing a polynomial hypergroup on N0. The basic facts on polynomial hypergroups and their characters can be found in the monograph [1] or in the papers [6, 7]. A recent review is [8]. The Banach space of almost periodic functions on hypergroups is introduced and studied by the author in [5]. Weakly almost periodic functions are the topic of [12]. It i...

In the past decade research on the multiresolution analysis has made considerable progress due to its wide applications. For the basic theory of multiresolution we refer readers to the work in 1, 2 . Recently, we find that a lot of authors try to extend the theory of wavelets on the Euclidean space to nilpotent Lie groups see 3–6 . In this paper we will give the definition of acceptable dilatio...

In this paper we define ?-independent (a weak-version of independence), Kronecker and dissociate sets on hypergroups and study their properties and relationships among them and some other thin sets such as independent and Sidon sets. These sets have the lacunarity or thinness property and are very useful indeed. For example Varopoulos used the Kronecker sets to prove the Malliavin theorem. In t...

we study topological von neumann regularity and principal von neumann regularity of banach algebras. our main objective is comparing these two types of banach algebras and some other known banach algebras with one another. in particular, we show that the class of topologically von neumann regular banach algebras contains all $c^*$-algebras, group algebras of compact abelian groups and cer...