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1
Content available remote Integral representations of bounded starlike functions
100%
Rønning F.
Annales Polonici Mathematici
|
1994-1995
|
tom 60
|
nr 3
289-297
EN
For α ≥ 0 let $ℱ_α$ denote the class of functions defined for |z| < 1 by integrating $1/(1-xz)^α$ if α > 0, and log(1/(1-xz)) if α = 0, against a complex measure on |x| = 1. We study families of starlike functions where zf'(z)/f(z) ranges over a parabola with given focus and vertex. We prove a number of properties of these functions, among others that they are bounded and that they belong to $ℱ_0$. In general, it is only known that bounded starlike functions belong to $ℱ_α$ for α > 0.
2
Content available Some results on convex meromorphic functions
80%
Ucar F. , Avci Y.
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
|
2019
|
tom 73
|
nr 1
EN
In this paper, we define a function \(F : D\times D\times D\to \mathbb{C}\) in terms of \(f\) and show that Re\(F > 0\) for all \(\zeta,z,w \in D\) if and only if \(f\) belongs to the class of convex meromorphic functions.
3
On some subclass of strongly starlike functions
80%
Jurasińska R. , Szpila A.
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
|
1998
|
tom z. 22 [170]
29-39
EN
In this paper for fixed natural number n we define subclass S*/n,(alpha) of strongly starlike functions [...].
4
Content available remote On the class of functions strongly starlike of order α with respect to a point
70%
Lecko A.
Annales Polonici Mathematici
|
1998
|
tom 68
|
nr 2
107-117
EN
We consider the class 𝓩(k;w), k ∈ [0,2], w ∈ ℂ, of plane domains Ω called k-starlike with respect to the point w. An analytic characterization of regular and univalent functions f such that f(U) is in 𝓩(k;w), where w ∈ f(U), is presented. In particular, for k = 0 we obtain the well known analytic condition for a function f to be starlike w.r.t. w, i.e. to be regular and univalent in U and have f(U) starlike w.r.t. w ∈ f(U).
5
Content available Fekete-Szegö inequalities associated withkthroot transformation based on quasi-subordination
70%
Magesh N. , Yamini J.
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
|
2017
|
tom 16
EN
Recently, Haji Mohd and Darus [1] revived the study of coefficient problems for univalent functions associated with quasi-subordination. Inspired largely by this article, we provide coefficient estimates with k-th root transform for certain subclasses of 𝒮 defined by quasi-subordination.
6
Content available Elementary examples of Loewner chains generated by densities
70%
Sola A.
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
|
2013
|
tom 67
|
nr 1
EN
We study explicit examples of Loewner chains generated by absolutely continuous driving measures, and discuss how properties of driving measures are reflected in the shapes of the growing Loewner hulls.
7
Content available remote Characterization of subclasses of univalent functions
60%
Trojnar-Spelina L.
Demonstratio Mathematica
|
2005
|
tom Vol. 38, nr 1
35--41
EN
We investigate the family of functions f(z) = z +(suma od n=2 do nieskończoności) anzn that are analytic in the unit disk with the property that the domain of values f(z) + 1+ei(alpha):2zf", (alpha is an element of (-pi,pi) is the parabolic region (Imw)2 < 2Rew - 1. Integral representation and convolution characterization are found and some coefficients bounds are given.
8
Content available remote On a problem H. S. Al-Amiri and M. O. Reade
60%
Singh S. , Gupta S.
Demonstratio Mathematica
|
2005
|
tom Vol. 38, nr 2
303--311
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.
9
Content available remote On the boundedness of the singh integral operator
60%
Miclăuş G.
Demonstratio Mathematica
|
2005
|
tom Vol. 38, nr 3
591--594
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.
10
Content available Coefficient bounds for some subclasses of p-valently starlike functions
60%
Selvaraj C. , Babu O. S. , Murugusundaramoorthy G.
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
|
2013
|
tom 67
|
nr 2
EN
For functions of the form \[f(z) = z^{p} + \sum_{n = 1}^{\infty} a_{p + n} z^{p + n}\] we obtain sharp bounds for some coefficients functionals in certain subclasses of starlike functions. Certain applications of our main results are also given. In particular, Fekete-Szego-like inequality for classes of functions defined through extended fractional differintegrals are obtained.
11
Some application of theGolusinvariation to the starlike functions with respect to m-symmetric points
60%
Stankiewicz J. , Szpila A.
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
|
2004
|
tom z. 27 [212]
61-68
EN
In this paper we consider the class of starlike functions with respect to m-symmetric points. Using the integral formula for functions from this class and applying the Golusin variation of the first type we obtain a sharp lower bound for If'(z)I.
12
Content available remote On classes of meromorphic or complex harmonic functions with a pole at the infinity
60%
Jakubowski Z. , Sibelska A.
Demonstratio Mathematica
|
2009
|
tom Vol. 42, nr 3
479-489
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].
13
Content available remote Remarks on the certain subclass of univalent functions
60%
Piejko K. , Trojnar-Spelina L.
Journal of Mathematics and Applications
|
2008
|
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.
14
Content available remote On partial sums of certain analytic functions
60%
Mostafa A.
Demonstratio Mathematica
|
2008
|
tom Vol. 41, nr 4
779-789
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.
15
The classes of functions which can be defined by subordination
60%
Jurasińska R. , Szpila A.
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
|
1998
|
tom z. 22 [170]
41-49
EN
Let H = H(U) be the class of all functions which are holomorphic in the unit disc U = {z : \z\ < 1}. Let P(n) denotes the class of all functions p(z) = 1+piz+... is an element H, such thatp(pz) -< (1+zn/(1-zn), where -< denotes subordination. With the class P(n) we connect the subclass S*(n) of starlike functions in the following way. A function f(z) = z + a2z + ... belongs to S* (n) if and only if zf'(z)/f(z) is an element of P(n). In this note we give the estimations of some coefficients in the classes P(n) and S*(n) and we find the radius of convexity of the class S*(n).
16
On bounded starlike functions
60%
Wiśniowska A.
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
|
1999
|
tom z. 23 [175]
167-173
EN
In this paper we investigate subclasses of starlike functions, where zf'(z)/f(z) is contained in conic domain with vertex at the origin. These classes of functions provide examples of bounded starlike functions.
17
Stability of convolution and dual sets for the class of k-uniformly convex and k-starlike functions
60%
Kanas S.
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
|
1998
|
tom z. 22 [170]
51-64
EN
Let k-UCV denote the class of k-uniformly convex functions and let k-ST be related class of k- starlike functions. Also, let f*g denote the Hadamard product (or convolution) of the analytic functions f and g, and V* denote the dual set of the set V. In this paper the classes k-UCV and k-ST in terms of dual sets are descibed. Duality of mentioned classes is also used to obtain other results in the class k-UCV and k-ST. Problem of neighbourhoods of functions as well as stability of convolution in the class k-UCV and k-ST are investigated.
18
Content available remote Stability of the Hadamard product of k-uniformly convex and k-starlike functions in certain neighbourhood
60%
Bednarz U.
Demonstratio Mathematica
|
2005
|
tom Vol. 38, nr 4
837--845
19
Content available remote On some subclass of strongly starlike functions
51%
Sokół J.
Demonstratio Mathematica
|
1998
|
tom Vol. 31, nr 1
81-86
20
Content available remote Fixed coefficients for certain subclasses of starlike functions with negative coefficients
51%
Aouf M. , Al-Dohiman A.
Demonstratio Mathematica
|
2005
|
tom Vol. 38, nr 3
551--565
EN
The main object of this paper is to study the class T*n,c(alfa,beta) of analytic functions with negative coefficients and with fixed second coefficients. Among other results of interest, we derive coefficient estimates, closure properties involving convex linear combinations, growth and distortion theorems, and radii of starlikeness and convexity for functions in the class T*n,c(alfa,beta). Many of these results are further extended to hold true for families of functions with finitely many fixed coefficients.
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