The k-ellipse is the plane algebraic curve consisting of all points whose sum of distances from k given points is a fixed number. The polynomial equation defining the k-ellipse has degree 2k if k is odd and degree 2k− ` k k/2 ́ if k is even. We express this polynomial equation as the determinant of a symmetric matrix of linear polynomials. Our representation extends to weighted k-ellipses and k-...

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...

Keywords: Meromorphic functions Multivalent functions Dziok–Srivastava linear operator Hadamard product (or convolution) Subordination between analytic functions Generalized hypergeometric function Symmetric points Conjugate points Symmetric conjugate points a b s t r a c t In the present paper, we introduce and investigate each of the following new subclasses: of meromorphically p-valent funct...

Global Krylov subspace methods are the most efficient and robust methods to solve generalized coupled Sylvester matrix equation. In this paper, we propose the nested splitting conjugate gradient process for solving this equation. This method has inner and outer iterations, which employs the generalized conjugate gradient method as an inner iteration to approximate each outer iterate, while each...

In this article, by making use of a q-analogue the familiar Borel distribution, we introduce two new subclasses: S?,?,q symmetric(b, A, B) and conjugate(b,A, starlike convex functions in open unit disk ? with respect to symmetric conjugate points. We obtain some properties including Taylor-Maclaurin coefficient estimates for each these subclasses deduce various corollaries consequences main res...