Approximating Convex Shapes With Respect to Symmetric Difference Under Homotheties

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.

Homotheties of Cylindrically Symmetric Static Manifolds and their Global Extension

Cylindrically symmetric static manifolds are classified according to their homotheties and metrics. In each case the homothety vector fields and the corresponding metrics are obtained explicitly by solving the homothety equations. It turns out that these metrics admit homothety groups Hm, where m = 4, 5, 7, 11. This classification is then used to identify the cylindrically symmetric static spac...

Characterization of Ellipses as Uniformly Dense Sets with Respect to a Family of Convex Bodies

Let K ⊂ R be a convex body containing the origin. A measurable set G ⊂ R with positive Lebesgue measure is said to be uniformly K-dense if, for any fixed r > 0, the measure of G ∩ (x + rK) is constant when x varies on the boundary of G (here, x + rK denotes a translation of a dilation of K). We first prove that G must always be strictly convex and at least C-regular; also, if K is centrally sym...

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...