On Differential Subordination of Higher-Order Derivatives of Multivalent Functions

Subordination for Higher-Order Derivatives of Multivalent Functions

Convolution and Differential Subordination for Multivalent Functions

The general classes of multivalent starlike, convex, close-to-convex and quasiconvex functions are introduced. These classes provide a unified treatment to various known subclasses. Inclusion and convolution properties are derived using the methods of convex hull and differential subordination. 1. Motivation and Preliminaries Let U = {z : |z| < 1} be the unit disk and H(U) be the class of all a...

Differential Subordination for Meromorphic Multivalent Quasi-convex Functions

We introduce new classes of meromorphic multivalent quasi-convex functions and find some sufficient differential subordination theorems for such classes in punctured unit disk with applications in fractional calculus.

Extension of Higher Order Derivatives of Lyapunov Functions in Stability Analysis of Nonlinear Systems

The Lyapunov stability method is the most popular and applicable stability analysis tool of nonlinear dynamic systems. However, there are some bottlenecks in the Lyapunov method, such as need for negative definiteness of the Lyapunov function derivative in the direction of the system’s solutions. In this paper, we develop a new theorem to dispense the need for negative definite-ness of Lyapunov...

On the higher-order derivatives of spectral functions

In this paper we are interested in the higher-order derivatives of functions of the eigenvalues of symmetric matrices with respect to the matrix argument. We describe the formula for the k-th derivative of such functions in two general cases. The first case concerns the derivatives of the composition of an arbitrary (not necessarily symmetric) k-times differentiable function with the eigenvalue...