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1
Content available remote Remarks on the certain subclass of univalent functions
100%
Piejko K. , Trojnar-Spelina L.
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tom Vol. 30
125-130
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.
2
Certain classes of multivalent functions with negative coefficients involving the Hadamard product
100%
Juma A. R. S.
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2012
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tom Vol. 18, nr 1
133-143
EN
In this paper, we introduce and investigate a new class of multivalent functions by using the Hadamard product structure defined in the open unit disk. We obtain coefficient estimates, a distortion theorem, extreme points and criteria of starlikeness and convexity for functions which belong to our class. Relevant connections of the results with those obtained in earlier works are also pointed out.
3
Content available remote Subclasses of univalent functions related with circular domains
84%
Trojnar-Spelina L.
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2011
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tom Vol. 34
109--116
EN
We investigate the family of functions normalized by the condition ƒ(0) = ƒ(0) - 1 = 0, that are analytic in the unit disk, with the property that the domain of values [...] is the disk |z-b| < b, b ≥ 1. Integral and convolution characterizations are found and coefficients bounds are given.
4
Content available remote A class of harminic starlike functions with respect to other points defined by Dziok-Srivastava operator
84%
Murugusundaramoorthy G. , Vijaya K. , Auof M. K.
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tom Vol. 30
113-124
EN
Making use of Dziok-Srivastava operator we introduced a new class of complex-valued harmonie functions which are orientation preserving, univalent and starlike with respect to other points. We investigate the coefficient bounds.distortion inequalities, extreme points and inclusion results for the generalized class of functions.
5
Content available remote Close-to-convexity properties of basic hypergeometric functions using their Taylor coefficients
84%
Raghavendar K. , Swaminathan A.
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2012
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tom Vol. 35
53--67
EN
In this paper, we find the conditions on parameters a, b, c and q such that the basic hypergeometric function zφ(a,b;c;q,z) and its q-Alexander transform are close-to-convex (and hence univalent) in the unit disc D:={z: |z|<1}.
6
Content available remote Inclusion relationship and Fekete-Szegö like inequalities for a subclass of meromorphic functions
84%
Răducanu D. , Orhan H. , Deniz E.
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2011
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tom Vol. 34
87--95
EN
In this paper using a differential operator, we define a new subclass of meromorphic functions. Sharp upper bounds for the functional […] in this class are obtained. An inclusion property is also given.
7
Content available remote On an application of certain sufficient condition for starlikeness
67%
Sokół J.
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tom Vol. 30
131-135
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.
8
Content available remote On certain properties of neighborhoods of analytic functions of complex order
67%
Latha S. , Poornima N.
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tom Vol. 30
83-90
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.
9
Content available remote Some parametric family of functions
67%
Dziok J.
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tom Vol. 29
99-107
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.
10
Content available remote Some inequalities involving differential operators and their applications to certain multivalent functions
67%
Dziok J. , Huseyin I. , Piejko K.
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tom Vol. 29
109-120
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].
11
Content available remote Stability of the integral transformation of k-uniformly convex and k-starlike functions
67%
Bednarz U.
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tom Vol. 29
91-98
EN
For a constant k ϵ [0, ∞) a normalized function f, analytic in the unit disk, is said to be k-uniformly convex if Re (1+z f" (z)/f'(z)) > k|zf"(z)/f'(z)| at any point in the unit disk. The class of k-uniformly convex functions is denoted k-UCV (cf. [8]). The function g is said to be k-starlike if g(z) = zf'(z) and f ϵ k-UCV. For analytic function f, where f(z) = z + a2z² + źźź the integral transformation is defined as follows: [wzór]. Generalized neighbourhood is defined as: [wzór]. In this note a problem of stability of the integral transformation of k-uniformly convex and k-starlike functions for TNδ neighbourhoods is investigated.
12
Content available Fekete-Szegö problems for certain class of analytic functions associated with quasi-subordination
67%
Sahoo P.
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tom Vol. 40
161--170
EN
In this paper, we determine the coefficient estimates and the Fekete-Szegö inequalities for [wzór], the class of analytic and univalent functions associated with quasi-subordination.
13
Content available An upper bound for third Hankel determinant of starlike functions related to shell-like curves connected with Fibonacci numbers
67%
Sokół J. , İlhan S. , Güney H. Ö.
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tom Vol. 41
195--206
EN
We investigate the third Hankel determinant problem for some starlike functions in the open unit disc, that are related to shell-like curves and connected with Fibonacci numbers. For this, firstly, we prove a conjecture, posed in [17], for sharp upper bound of second Hankel determinant. In the sequel, we obtain another sharp coefficient bound which we apply in solving the problem of the third Hankel determinant for these functions.
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