Spectral theory and scattering theory on non-compact manifolds with ends of various shapes have had a huge influence on mathematics and physics. One important and extensively studied family consists of manifolds with hyperbolic cusps. These manifolds first appeared in mathematics in the context of number theory as quotients of the upper half plane by arithmetic lattices. It was discovered that ...

This paper is concerned with the differential subordination properties of multivalent functions involving by generalized integral operator. We investigate some applications a results for normalized analytic function ( ) and operator on class all functions. Some our previously known results. Keywords — Analytic functions; p–valent; operator; subordination.