‎In this paper first we define the morphism between geometric spaces in two different types‎. ‎We construct two categories of $uu$ and $l$ from geometric spaces then investigate some properties of the two categories‎, ‎for instance $uu$ is topological‎. ‎The relation between hypergroups and geometric spaces is studied‎. ‎By constructing the category $qh$ of $H_{v}$-groups we answer the question...

‎in this paper first we define the morphism between geometric spaces in two different types‎. ‎we construct two categories of $uu$ and $l$ from geometric spaces then investigate some properties of the two categories‎, ‎for instance $uu$ is topological‎. ‎the relation between hypergroups and geometric spaces is studied‎. ‎by constructing the category $qh$ of $h_{v}$-groups we answer the question...

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...

We introduce a family of hypergroups, called weakly complete, generalizing the construction complete hypergroups. Starting from given group G, our prescribes β-classes hypergroups and allows some hyperproducts not to be parts, based on suitably defined relation over G. The commutativity degree can related that underlying group. Furthermore, in analogy commutativity, we completeness finite analy...

The concept of semi-bounded generalized hypergroups (SBG hypergroups) is developed which are more special then generalized hypergroups introduced by Obata and Wildberger and which are more general then discrete hypergroups or even discrete signed hypergroups. The convolution of measures and functions is studied. In case of commutativity we define the dual objects and prove some basic theorems o...

Polynomial hypergroups are a very interesting class of hypergroups with a great variety of examples which are quite different from groups. So the L-algebras of hypergroups have properties very distinguished to the L-algebras of groups, in particular in the context of amenability and related conditions. Being amenable the L-algebra of an abelian group does not possess any non-zero bounded point ...

In this paper, we show a new construction of hypergroups that, under appropriate conditions, are complete or non-complete 1-hypergroups. Furthermore, classify the 1-hypergroups size 5 and 6 based on partition induced by fundamental relation ?. Many these can be obtained using aforesaid hypergroup construction.

In this paper, we extend the notion of semi-hypergroups (resp. hypergroups) to neutro-semihypergroups neutro-hypergroups). We investigate property anti-semihypergroups anti-hypergroups). also give a new alternative neutro-hyperoperations anti-hyperoperations), neutro-hyperoperation-sophications anti-hypersophications). Moreover, show that these concepts are different from classical by several e...

The aimof this paper is to introduce the notion of generalmutually associative hypergroups and to give some properties of the hypergroups associated with binary relations related to these notions. A program written in C# computes the number of Rosenberg hypergroups that satisfies the property of (general) mutual associativity. © 2010 Elsevier Ltd. All rights reserved.

Hypergroups can be subdivided into two large classes: those whose heart coincide with the entire hypergroup and in which is a proper sub-hypergroup. The latter class includes family of 1-hypergroups, reduces to singleton, therefore trivial group. However, very little known about hypergroups that are neither 1-hypergroups nor belong first class. goal this work take step classifying G-hypergroups...