In this work, some generalized Euclidean operator radius inequalities are established. Refinements of well-known results provided. Among others, bounds in terms the Cartesian decomposition a given Hilbert space proven.

By Poincaré operators we mean the translation operator along the trajectories of the associated differential system and the first return (or section) map defined on the cross section of the torus by means of the flow generated by the vector field. The translation operator is sometimes also called as Poincaré–Andronov or Levinson or, simply, T -operator. In the classical theory (see [K], [W], [Z...

by using generalized salagean differential operator a newclass of univalent holomorphic functions with fixed finitely manycoefficients is defined. coefficient estimates, extreme points,arithmetic mean, and weighted mean properties are investigated.