we study a new class of $h_v$-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.

We study a new class of $H_v$-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.

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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 thet...