On the definition of a close-to-convex function.
On the derivative of hyperbolically convex functions.
On the extreme points of some classes of holomorphic functions.
On the extreme points of subordination families
We investigate extreme points of some classes of analytic functions defined by subordination and classes of functions with varying argument of coefficients. By using extreme point theory we obtain coefficient estimates and distortion theorems in these classes of functions. Some integral mean inequalities are also pointed out.
On the Fekete-Szegö problem.
On the Fekete-Szegö problem for some subclasses of analytic functions.
On the Fekete-Szegő theorem for close-to-convex functions.
On the Hadamard products of schlicht functions and applications.
On the Hankel determinants of close-to-convex univalent functions.
On the Hardy class of certain subclass of Bazilevič function
On the John Constant.
On the logarithmic derivative of some Bazilevic functions.
On the maximum of and some related functionals for bounded real univalent functions
On the -uniformly close to convex functions with respect to a convex domain.
On the order of convolution consistence of the analytic functions with negative coefficients
Making use of a modified Hadamard product, or convolution, of analytic functions with negative coefficients, combined with an integral operator, we study when a given analytic function is in a given class. Following an idea of U. Bednarz and J. Sokół, we define the order of convolution consistence of three classes of functions and determine a given analytic function for certain classes of analytic functions with negative coefficients.
On the order of starlikeness and convexity of complex harmonic functions with a two-parameter coefficient condition
The article of J. Clunie and T. Sheil-Small [3], published in 1984, intensified the investigations of complex functions harmonic in the unit disc Δ. In particular, many papers about some classes of complex mappings with the coefficient conditions have been published. Consideration of this type was undertaken in the period 1998-2004 by Y. Avci and E. Złotkiewicz [2], A. Ganczar [5], Z. J. Jakubowski, G. Adamczyk, A. Łazińska and A. Sibelska [1], [8], [7], H. Silverman [12] and J. M. Jahangiri [6],...
On the (p, q)-type and lower (p, q)-type of an entire function.
On the radius of convexity for a class of conformal maps
Let 𝓐 denote the class of all analytic functions f in the open unit disc 𝔻 in the complex plane satisfying f(0) = 0, f'(0) = 1. Let U(λ) (0 < λ ≤ 1) denote the class of functions f ∈ 𝓐 for which |(z/f(z))²f'(z) -1| < λ for z ∈ 𝔻. The behaviour of functions in this class has been extensively studied in the literature. In this paper, we shall prove that no member of U₀(λ) = {f ∈ U(λ): f''(0) = 0} is convex in 𝔻 for any λ and obtain a lower bound for the...
On the radius of convexity of some family of functions regular in the ring 0 < |z| < 1
On the radius of starlikeness and convexity of certain classes of analytic functions