  The aim of the present paper is to provide an \emph{intrinsic} investigation
of special Finsler spaces of $H_{p}$-scalar curvature and of $H_{p}\,$-constant
curvature. Characterizations of such spaces are shown. Sufficient condition for
Finsler space of $H_{p}$-scalar curvature to be of perpendicular scalar
curvature is investigated. Necessary and sufficient condition under which a
Finsler space of scalar curvature turns into a Finsler space of $H_{p}$-scalar
curvature is given. Further, certain conditions under which a Finsler manifolds
of $H_{p}$-scalar curvature and of scalar curvature reduce to a Finsler
manifold of $H_{p}$-constant curvature are obtained. Finally, various examples
are studied and constructed.
