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1
Content available remote Length problems for Bazilevič functions
Nunokawa Mamoru, Sokół Janusz, Tang Huo
Demonstratio Mathematica
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2019
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Vol. 52, nr 1
56--60
EN
Let C(r) denote the curve which is image of the circle |z|=r<1 under the mapping f. Let L(r) be the length of C(r) and A(r) the area enclosed by the curve C(r). Furthermore M(r) = max|z|=r |f(z)|. We present some relations between these notions for Bazilevič functions.
2
Content available An upper bound for third Hankel determinant of starlike functions related to shell-like curves connected with Fibonacci numbers
Sokół J., İlhan S., Güney H. Ö.
Journal of Mathematics and Applications
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2018
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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.
3
Content available Majorization problems for classes of analytic functions
Dziok J., Murugusundaramoorthy G., Janani T
Journal of Mathematics and Applications
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2015
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Vol. 38
49--57
EN
The main object of the present paper is to investigate problems of majorization for certain classes of analytic functions of complex order defined by an operator related to the modified Bessel functions of first kind. These results are obtained by investigating appropriate class of admissible functions. Various known or new special cases of our results are.
4
Content available remote Convolution properties of subclasses of analytic functions associated with the Dziok-Srivastava operator
Goyal S. P., Bansal S. K., Goswami P., Wang Z.-G.
Journal of Mathematics and Applications
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2013
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Vol. 36
71--77
EN
The aim of this paper is to introduce two new classes of analytic function by using principle of subordination and the Dziok-Srivastava operator. We further investigate convolution properties for these calsses. We also nd necessary and sufficient condition and coefficient estimate for them.
5
Content available remote Applications of convolution properties
Trojnar-Spelina L.
Demonstratio Mathematica
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2013
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Vol. 46, nr 3
513--523
EN
K. I. Noor (2007 Appl. Math. Comput. 188, 814–823) has defined the classes Qk(a, b, λ, γ) and Tk(a, b, λ, γ) of analytic functions by means of linear operator connected with incomplete beta function. In this paper, we have extended some of the results and have given other properties concerning these classes.
6
Content available remote Close-to-convexity properties of basic hypergeometric functions using their Taylor coefficients
Raghavendar K., Swaminathan A.
Journal of Mathematics and Applications
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2012
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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}.
7
Content available remote Subclasses of univalent functions related with circular domains
Trojnar-Spelina L.
Journal of Mathematics and Applications
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2011
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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.
8
Content available remote Inclusion relationship and Fekete-Szegö like inequalities for a subclass of meromorphic functions
Răducanu D., Orhan H., Deniz E.
Journal of Mathematics and Applications
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2011
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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.
9
Content available remote Application of generalized Ruscheweyh derivatives on p-valent functions
Parihar H. S., Agarwal R.
Journal of Mathematics and Applications
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2011
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Vol. 34
75--86
EN
In this paper, we define a new class of p-valent analytic functions with finitely many coefficients by making use of the generalized Ruscheweyh derivatives involving a general fractional derivative operator. Some properties of this class are also investigated. e.g. Coefficient estimates, convex combination, arithmatic mean, extreme points, radii of starlikeness and convexity. Many known results are as a special case of our results.
10
Content available remote On T-neighborhoods of analytic functions
Bednarz U., Sokół J
Journal of Mathematics and Applications
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2010
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Vol. 32
25-32
11
Content available remote On a starlikeness of order α condition for meromorphic m-valent functions
Catas A.
Journal of Mathematics and Applications
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2010
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Vol. 33
5-11
EN
The aim of the paper is to provide sufficient conditions for starlikeness of order α for meromorphic m-valent functions in the punctured disc. The present work is based on some results invoving differential subordinations.
12
Content available remote On a certain class of analytic functions involving hypergeometric functions
Khosravianarab Sh., Kulkarni S. R., Raina R. K.
Journal of Mathematics and Applications
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2010
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Vol. 32
53-61
EN
A certain class of functions analytic in the open unit disk and defined in terms of hypergeometric functions is introduced and investigated. We establish starlikeness, convexity and spirallikeness properties for this class of functions. Special cases and some useful consequences of our main results are aslo mentioned.
13
Content available remote Properties of analytic functions defined by an integral operator
Cotîrlă L. I.
Demonstratio Mathematica
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2010
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Vol. 43, nr 4
799-803
EN
In this paper we present some properties for the analytic functions in the open unit disc U defined by an integral operator.
14
Content available remote New sufficient conditions for starlikeness of analytic functions involving a fractional differintegral operator
Prajapat J. K., Raina R. K.
Demonstratio Mathematica
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2010
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Vol. 43, nr 4
805-813
EN
In this paper we apply a fractional differintegral operator to a class of analytic functions and derive certain new sufficient conditions for the starlikeness of this class of functions. The usefulness of the main results are depicted by deducing several interesting corollaries and relevances with some of the earlier results are also pointed out.
15
Content available remote Subordinations and superordinations using the Dziok-Srivastava linear operator
Oros G. I., Oros O.
Journal of Mathematics and Applications
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2009
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Vol. 31
99-106
EN
By using the properties of the Dziok-Srivastava linear operator we obtain differential subordinations and superordinations by using functions from class A. A sandwich-type result is also given. Theorem 1 from the paper gives sufficient conditions such that a function f ∈ A to be starlike, convex and α-convex.
16
Content available remote Coefficient conditions for univalency and starlikeness of analytic functions
Mondal S. R., Swaminathan A.
Journal of Mathematics and Applications
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2009
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Vol. 31
77-90
EN
In this paper, we find conditions on the coefficients {a(k)} such that the corresponding analytic function f(z) and its partial sum fn(z) are close-to-convex with respect to some starlike function in the unit disc D. We also find conditions on these coefficients so that the analytic function is starlike univalent in D. As an application, we find conditions on the triplet (a, b, c) so that, the normalized Gaussian hypergeometric function and its particular cases, are in one of these classes.
17
Content available remote Certain sufficienty conditions on Fox-Wright function
Chaurasia V., Parihar H.
Demonstratio Mathematica
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2008
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Vol. 41, nr 4
813-822
EN
The main object of this paper is to find certain conditions for the function [...] to be a member of certain subclasses of analytic functions. Our results provides generalization of some recent results due to Swaminathan [19] and Chaurasia and Srivastava [20].
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