Convex Hamiltonians without Conjugate Points

Some Properties of Certain Subclasses of Close-to-Convex and Quasi-convex Functions with Respect to 2k-Symmetric Conjugate Points

Starlike Functions of order α With Respect To 2(j,k)-Symmetric Conjugate Points

In this paper, we introduced and investigated starlike and convex functions of order α with respect to 2(j,k)-symmetric conjugate points and coefficient inequality for function belonging to these classes are provided . Also we obtain some convolution condition for functions belonging to this class.

A Geometric Proof of the Existence of the Green Bundles

We give a new proof of the existence of the Green bundles. Let (M, g) be a compact Riemannian manifold, and denote by gt its geodesic flow on the tangent bundle TM . Let π : TM → M be the canonical projection and for all θ ∈ TM let V (θ) be the kernel of dπθ. Two points θ1, θ2 are said to be conjugate if θ2 = gtθ1 and dgtV (θ1) ∩ V (θ2) 6= 0. It was proved by Hopf [5] that a two-dimensional tor...

Convolutions of meromorphic multivalent functions with respect to n-ply points and symmetric conjugate points

It is well-known that the classes of starlike, convex and close-to-convex univalent functions are closed under convolution with convex functions. In this paper, closure properties under convolution of general classes of meromorphic p-valent functions that are either starlike, convex or close-to-convex with respect to n-ply symmetric, conjugate and symmetric conjugate points are investigated. 20...

Convex Optimal Control Problems with Smooth Hamiltonians

Optimal control problems with convex costs, for which Hamiltonians have Lipschitz continuous gradients, are considered. Examples of such problems, including extensions of the linear-quadratic regulator with hard and possibly state-dependent control constraints, and piecewise linear-quadratic penalties are given. Lipschitz continuous differentiability and strong convexity of the terminal cost ar...