Retraction Note to: Toeplitz Matrices Whose Elements are the Coefficients of Starlike and Close-to-Convex Functions

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

Noncirculant Toeplitz Matrices All of Whose Powers Are Toeplitz

Let a, b and c be fixed complex numbers. Let Mn(a, b, c) be the n×n Toeplitz matrix all of whose entries above the diagonal are a, all of whose entries below the diagonal are b, and all of whose entries on the diagonal are c. For 1 6 k 6 n, each k × k principal minor of Mn(a, b, c) has the same value. We find explicit and recursive formulae for the principal minors and the characteristic polyno...

Uniformly Starlike and Convex Functions with Negative Coefficients

Let A(ω) be the class of analytic functions of the form: f(z) = (z − ω) + ∞ ∑ k=2 ak(z − ω) defined on the open unit disk U = {z : |z| < 1} normalized with f(ω) = 0, f ′(ω)−1 = 0 and ω is an arbitrary fixed point in U. In this paper, we define a subclass of ω − α − uniform starlike and convex functions by using a more generalized form of Ruschewey derivative operator. Several properties such as...

Initial coefficients of starlike functions with real coefficients

The sharp bounds for the third and fourth coefficients of Ma-Minda starlike functions having fixed second coefficient are determined. These results are proved by using certain constraint coefficient problem for functions with positive real part whose coefficients are real and the first coefficient is kept fixed. Analogous results are obtained for a general class of close-to-convex functions

On Certain Multivalent Starlike or Convex Functions with Negative Coefficients