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1
Content available remote Fourth Hankel and Toeplitz determinants for a subclass of analytic functions subordinate to 1+sin(z)
Ganesh Koride, Rayaprolu Bharavi Sharma, Saroja Kasula, Yakaiah Koneti
Mathematica Applicanda
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2023
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Vol. 51, no. 2
321--338
EN
The purpose of the present paper is to determine the coefficient bounds, fourth Hankel determinants, Toeplitz determinants for the function f in a subclass of analytic functions subordinate to 1+sin(z). We also study the Fekete-Szegö inequality and Zalcman conjecture for functions in this class.
PL
Celem tego badania jest ustalenie oszacowań współczynników wyznaczników Hankela czwartego rzędu oraz wyznaczników Toeplitza dla funkcji należących do podklasy funkcji analitycznych podporządkowanych wyrażeniu 1 + sin z. Dodatkowo, analizujemy nierówność Fekete-Szegő-Szegő oraz hipotezę Zalcmana dla funkcji w tejże klasie.
2
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.
3
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.
4
Content available Fekete-Szegö problems for certain class of analytic functions associated with quasi-subordination
Sahoo P.
Journal of Mathematics and Applications
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2017
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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.
5
Content available Starlikeness and convexity of certain integral operators defined by convolution
Aggarwal J., Mathur R.
Journal of Mathematics and Applications
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2015
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Vol. 38
5--13
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.
6
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.
7
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.
8
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}.
9
Certain classes of multivalent functions with negative coefficients involving the Hadamard product
Juma A. R. S.
Journal of Applied Analysis
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2012
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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.
10
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.
11
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.
12
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.
13
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
14
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.
15
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.
16
Content available remote A new class of analytic functions based on Ruscheweyh derivative
Sudharsan T. V., Thirumalaisamy R., Sivasubramanian S., Subramanian K. G.
Journal of Mathematics and Applications
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2010
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Vol. 33
103-115
EN
In this paper we introduce a new class [formula/wzór] consisting of analytic functions with negative coeffcients and investigate various properties and characterization of the class. The results include coeffcient estimates, distortion theorem, closure theorems and integral operators for the class [formula/wzór]. Also radii of close-to-convexity, starlikeness and convexity are determined.
17
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.
18
Content available remote Subordination results and integral means inequalities for generalized k-starlike functions
Dziok J., Murugusundaramoorthy G., Wiśniowska W.
Journal of Mathematics and Applications
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2009
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Vol. 31
37-49
EN
In the paper, we introduce a generalized class of k-starlike functions associated with Wright generalized hypergeometric functions and obtain the sequential subordination results and integral means inequalities. Some interesting consequences of our results are also pointed out.
19
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.
20
Content available remote Remarks on the certain subclass of univalent functions
Piejko K., Trojnar-Spelina L.
Journal of Mathematics and Applications
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2008
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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.
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