scholarly journals Convexity of Certainq-Integral Operators ofp-Valent Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
K. A. Selvakumaran ◽  
S. D. Purohit ◽  
Aydin Secer ◽  
Mustafa Bayram
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Integral Operators ◽  
Special Cases ◽  
Convexity Properties

By applying the concept (and theory) of fractionalq-calculus, we first define and introduce two newq-integral operators for certain analytic functions defined in the unit disc𝒰. Convexity properties of theseq-integral operators on some classes of analytic functions defined by a linear multiplier fractionalq-differintegral operator are studied. Special cases of the main results are also mentioned.

scholarly journals Certain Subclasses of Multivalent Functions Defined by Higher-Order Derivative

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Xiaofei Li ◽  
Deng Ding ◽  
Liping Xu ◽  
Chuan Qin ◽  
Songbo Hu
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Extreme Points ◽  
Higher Order ◽  
Order Derivative ◽  
Special Cases ◽  
Higher Order Derivative ◽  
Coefficient Inequalities ◽  
Distortion Theorems

In this paper, we define and study some subclasses of multivalent analytic functions of higher order in the unit disc. These classes generalize some classes previously studied. We obtain coefficient inequalities, distortion theorems, extreme points, and integral mean inequalities. We derive some results as special cases.

scholarly journals Geometric properties of some linear operators defined by convolution

2008 ◽  
Vol 39 (4) ◽  
pp. 325-334 ◽  
Author(s):  
R. Aghalary ◽  
A. Ebadian ◽  
S. Shams
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Integral Transform ◽  
Integral Transforms ◽  
Linear Operators ◽  
Geometric Properties ◽  
Special Cases ◽  
Classical Integral ◽  
Alpha Beta

Let $\mathcal{A}$ denote the class of normalized analytic functions in the unit disc $ U $ and $ P_{\gamma} (\alpha, \beta) $ consists of $ f \in \mathcal{A} $ so that$ \exists ~\eta \in \mathbb{R}, \quad \Re \bigg \{e^{i\eta} \bigg [(1-\gamma) \Big (\frac{f(z)}{z}\Big )^{\alpha}+ \gamma \frac{zf'(z)}{f(z)} \Big (\frac{f(z)}{z}\Big )^{\alpha} - \beta\bigg ]\bigg \} > 0. $ In the present paper we shall investigate the integral transform$ V_{\lambda, \alpha}(f)(z) = \bigg \{\int_{0}^{1} \lambda(t) \Big (\frac{f(tz)}{t}\Big )^{\alpha}dt\bigg \}^{\frac{1}{\alpha}}, $ where $ \lambda $ is a non-negative real valued function normalized by $ \int_{0}^{1}\lambda(t) dt=1 $. Actually we aim to find conditions on the parameters $ \alpha, \beta, \gamma, \beta_{1}, \gamma_{1} $ such that $ V_{\lambda, \alpha}(f) $ maps $ P_{\gamma}(\alpha, \beta) $ into $ P_{\gamma_{1}}(\alpha, \beta_{1}) $. As special cases, we study various choices of $ \lambda(t) $, related to classical integral transforms.

scholarly journals Functions starlike with respect to other points

1991 ◽  
Vol 14 (3) ◽  
pp. 451-456 ◽  
Author(s):  
S. Abdul Halim
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disc ◽  
The Real ◽  
Symmetric Points ◽  
Class Of Functions

In [7], Sakaguchi introduce the class of functions starlike with respect to symmetric points. We extend this class. Forp≤β<1, letSS*(β)be the class of normalised analytic functionsfdefined in the open unit discDsuch thatRezf′(z)/(f(z)−f(−z))>β, for somez ϵ D. In this paper, we introduce 2 other similar classesSC*(β),SSC*(β)as well as give sharp results for the real part of some function forf ϵ SS*(β),SC*(β)andSSC*(β)The behaviour of certain integral operators are also considered.

scholarly journals ON A CLASS OF ANALYTIC FUNCTIONS INVOLVING THE SALAGEAN DIFFERENTIAL OPERATOR

1992 ◽  
Vol 23 (1) ◽  
pp. 51-58
Author(s):  
S. ABDUL HALIM
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Unit Disc ◽  
Integral Operators

Weintroduce the class $B_n(\alpha$) consisting of functions.analytic in the unit disc. In this paper, we give some properties of this class as well as considering some integral operators.

scholarly journals Convexity and Spirallikeness Conditions for Two New General Integral Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
H. Özlem Güney ◽  
Serap Bulut
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
General Integral

We define two new general integral operators for certain analytic functions in the unit disc and give some sufficient conditions for these integral operators on some subclasses of analytic functions.

scholarly journals Certain Properties of a Generalized Class of Analytic Functions Involving Some Convolution Operator

2021 ◽  
pp. 49-76
Author(s):  
Faroze Ahmad Malik ◽  
Nusrat Ahmed Dar ◽  
Chitaranjan Sharma
Keyword(s):  
Convex Functions ◽  
Convolution Operator ◽  
Analytic Functions ◽  
Extreme Points ◽  
Integral Operators ◽  
Integral Means ◽  
Coefficient Bounds ◽  
Complex Order ◽  
Special Cases ◽  
The Family

We use the concept of convolution to introduce and study the properties of a unified family $\mathcal{TUM}_\gamma(g,b,k,\alpha)$, $(0\leq\gamma\leq1,\,k\geq0)$, consisting of uniformly $k$-starlike and $k$-convex functions of complex order $b\in\mathbb{C}\setminus\{0\}$ and type $\alpha\in[0,1)$. The family $\mathcal{TUM}_\gamma(g,b,k,\alpha)$ is a generalization of several other families of analytic functions available in literature. Apart from discussing the coefficient bounds, sharp radii estimates, extreme points and the subordination theorem for this family, we settle down the Silverman's conjecture for integral means inequality. Moreover, invariance of this family under certain well-known integral operators is also established in this paper. Some previously known results are obtained as special cases.

scholarly journals Convexity Properties for Certain Classes of Analytic Functions Associated with an Integral Operator

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Ben Wongsaijai ◽  
Nattakorn Sukantamala
Keyword(s):  
Integral Operator ◽  
Analytic Functions ◽  
Integral Operators ◽  
Convexity Properties ◽  
New Form

We introduce a new form of generalized integral operator defined on the class of analytic functionsA0. By making use of this novel integral operator, we give the convexity of other integral operators. We also briefly indicate the relevant connections of our presented results to the formerly reported results. Furthermore, other interesting properties are also discussed.

scholarly journals A note on Bazilevič functions

1991 ◽  
Vol 14 (4) ◽  
pp. 821-823 ◽  
Author(s):  
S. A. Halim ◽  
D. K. Thomas
Keyword(s):  
Lower Bound ◽  
Analytic Functions ◽  
Unit Disc ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disc ◽  
Iterated Integral ◽  
Bazilevic Functions ◽  
Sharp Lower Bound

Forα>0, letB1(α)be the class of normalized analytic functions defined in the open unit discDsatisfyingRe(f(z)/z)α−1f′(z)>0forz∈D. The sharp lower bound forRe(f(z)/z)αis obtained and the result is generalized to some iterated integral operators.

scholarly journals Generalizedk-Uniformly Close-to-Convex Functions Associated with Conic Regions

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Khalida Inayat Noor
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Unit Disc ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disc ◽  
Coefficient Problems ◽  
Multiplier Transformation ◽  
Inclusion Results

We define and study some subclasses of analytic functions by using a certain multiplier transformation. These functions map the open unit disc onto the domains formed by parabolic and hyperbolic regions and extend the concept of uniformly close-to-convexity. Some interesting properties of these classes, which include inclusion results, coefficient problems, and invariance under certain integral operators, are discussed. The results are shown to be the best possible.

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