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EN
This paper considers the following problem: for what value r, r < 1 a function that is univalent in the unit disk |z| < 1 and convex in the disk |z| < r becomes starlike in |z| < 1. The number r is called the radius of convexity sufficient for starlikeness in the class of univalent functions. Several related problems are also considered.
EN
We investigate classes of k-uniformly convex functions which generalize the class UCV introduced by Goodman in 1991. We solve the problem of finding the largest α ≥ 0 such that the class of k-uniformly convex functions is contained in the class of starlike functions of order α.
EN
We define two new general integral operators for certain analytic functions in the unit disc U and give some sufficient conditions for these integral operators on some subclasses of analytic functions.
EN
In this paper we define classes of harmonic functions related to the Janowski functions and we give some necessary and sufficient conditions for these classes. Some topological properties and extreme points of the classes are also considered. By using extreme points theory we obtain coefficients estimates, distortion theorems, integral mean inequalities for the classes of functions.
5
EN
In this article we investigate some classes of meromorphic or complex harmonie functions with a pole, which are generated either by analytic conditions or by "coefficient inequalities". There are given theorems, which combine the geometrical properties of functions of the introduced classes. Some results broaden knowledge about the classes of functions, which were investigated in [15]. The main inspiration for the reaserch were the papers [4] and [11]. The part of results were presented in the XII-th International Mathematically-Informatical Conference in Chełm (2nd-5th July, 2006) [12].
6
Content available remote Remarks on the certain subclass of univalent functions
EN
We investigate the family LP α (α ∈ (-π, π]) of functions [wzór] that are analytic in the unit disk with the property that the domain of values [wzór] is the parabolic region (Imw) ² < 2Rew - 1.We give inclusion theorems and bounds of Re �'(z) for this class.
7
Content available remote On certain properties of neighborhoods of analytic functions of complex order
EN
Let A(n) denote the class of functions of the form [wzór] which are analytic in the open unit disk U = {z : |z| < 1}. In this note, the subclasses Sn (β, γ, a, c), Rn (β, γ, a, c; μ ), S(sup α) (sub n) (β, γ a, c) and R (sup α) (sub n) (β, γ, a, c; μ ) of A(n)(are defined and some properties of neighborhoods arę studied for functions of complex order in these classes.
8
Content available remote On an application of certain sufficient condition for starlikeness
EN
In this paper we consider a sufficient condition for furiction to be a-starlike function, when α ∈ [0, 1/2]. We use it for certain subclass of strongly starlike functions defined by a geometric condition. We take advantage of the techniąues of differential subordinations.
EN
The aim of this paper is to obtain coefficient estimates, distortion theorem, extreme points and radii of close - to - convexity, starlikeness and convexity for functions belonging to the subclass TSlambda (n,alpha, beta) of uniformly convex functions with negative coefficients. We also derive many results for the modified Hadamard products of functions belonging to the class TSlambda(n,alpha, beta), and obtain several interesting distortion theorems for certain fractional operators of functions in this class. Finally, we consider integral operators associated with functions in this class.
10
Content available remote On partial sums of certain analytic functions
EN
In the present paper we give some results concerning partial sums of certain analytic functions analogous to the results due to H. Silverman [J. Math. Anal. Appl. 209 (1997), 221-227]. All the results are sharp.
11
Content available remote Some parametric family of functions
EN
In the paper, we define classes of analytic functions, in terms of some linear operator. Coefficients estimates, distortion theorems, and the radii of convexity and starlikeness for this class of analytic functions are given here.
EN
The main object of the present paper is to investigate several results of certain differential operators which were recently introduced and (or) studied in a series of papers by Chen et et al. [1-3], Irmak et al. [8, 10, 11], Dziok et al. [5, 6] and Liu et al. [14]. In addition, some applications of our results involving certain differential inequalities of multivalently analytic and (or) multivalently raeromorphic functions are given. Our certain results also include some recent results in [5, 6, 9, 11, 12].
13
Content available remote Some relations including various linear operators
EN
Making use of the Carlson-Schaer linear operator, some subclasses of analytic functions are studied. Some relations including various linear operators are given.
14
Content available remote On certain subclasses of p-valently analytic functions of order alpha
EN
The object of the present paper is to derive various properties and char- acteristics of certain subclasses of p-valently analytic functions of order alpha in the open unit disc by using the techniques involving the Briot-Bouquet differential subordination.
15
Content available remote On sufficient condition for starlikeness of certain integral of analytic function
EN
The author aims at finding certain condition on Re f' which is sufficient for the function Φ(z) = ∫(sup z)(sub 0) (sup f(t))(sub t)dt to be starlike function.
16
Content available remote Radius problems for a class of analytic functions
EN
In this present paper, we investigate certain radius problems for a class of normalized analytic functions in the open unit disk in the complex plane.
EN
In 1984 J. Clunie and T. Sheil-Small initiated studies of complex functions harmonic in the unit disc. In 1987 W. Hergartner and G. Schober considered mappings of this type, defined in the domain U = {z is an element of C : \z\ > 1}. Several mathematicians examine classes of complex harmonic functions with some coefficient conditions, defined in the unit disc (e.g. [2], [5], [10], [1] [9]) or in U (e.g. [8], [7]). We investigate the classes of mappings harmonic in U with coefficient conditions more general than the considered in paper [8].
19
Content available remote On the boundedness of the singh integral operator
EN
In this paper we determine some conditions so that the Singh integral operator (1) and thier iterative, when it is applied to functions subordinate at starlike functions, are bounded in U.
20
Content available remote On a problem H. S. Al-Amiri and M. O. Reade
EN
In the present paper, the authors investigate the univalence of the functions f, analytic in -E, f(O) = 0, f'(0) = 1 and which satisfy Re [(1 - alfa)f'(z) + alfa (1+ zf''(z): f'(z)] >beta, z is an element of E, where alfa > 0 and 0 < beta < 1. The univalence of such functions has already been established in the case when alfa < 0 and beta = 0 by H. S. Al-Amiri and M. 0. Reade in 1975.
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