Associated (semi)hypergroups from Duplexes

ASSOCIATED (SEMI)HYPERGROUPS FROM DUPLEXES

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.

Generalized hypergroups and orthogonal polynomials

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...

On weak Γ-(semi)hypergroups

The associated measure on locally compact cocommutative KPC-hypergroups

We study harmonic analysis on cocommutative KPC-hyper-groups‎, which is a generalization of DJS-hypergroups‎, ‎introduced by Kalyuzhnyi‎, ‎Podkolzin and Chapovsky‎. ‎We prove that there is a relationship between‎ ‎the associated measures $mu$ and $gamma mu$‎, ‎where $mu$ is‎ ‎a Radon measure on KPC-hypergroup $Q$ and $gamma$ is a character on $Q$.

HX-hypergroups associated with the direct products of some ${bf Z}/n {bf Z}$

One studies the $HX$-hypergroups, corresponding to the Chinese hypergroups associated with the direct products of some ${bf Z}/n {bf Z},$ calculating their fuzzy grades.