hopes

The largest class of hyperstructures is the Hv-structures, introduced in 1990, which proved to have a lot of applications in mathematics and several applied sciences, as well. Hyperstructures are used in the Lie-Santilli theory focusing to the hypernumbers, called e-numbers. We present the appropriate e-hyperstuctures which are defined using any map, in the sense the derivative map, called theta-hyperstructures.

We study a new class of Hv -structures called Fundamentally Very Thin. This is an extension of the well known class of the Very Thin hyperstructures. We present applications of these hyperstructures.

Abstract. The largest class of hyperstructures is the one which satisfy the weak properties. These are called Hv-structures introduced in 1990 and they proved to have a lot of applications on several applied sciences. In this paper we present an introduction on the special classes of hyperstructures used inthe Lie-Santilli theory called e-hyperstructures. Several extensions of these hyperstructures are also presented