Convexity of area integral means for analytic functions

2016 ◽  
Vol 62 (3) ◽  
pp. 307-317 ◽  
Author(s):  
Weiqiang Peng ◽  
Chunjie Wang ◽  
Kehe Zhu
Keyword(s):  
Analytic Functions ◽  
Integral Means ◽  
Area Integral

Area Integral Means of Analytic Functions in the Unit Disk

2018 ◽  
Vol 61 (3) ◽  
pp. 509-517 ◽  
Author(s):  
Xiaohui Cui ◽  
Chunjie Wang ◽  
Kehe Zhu
Keyword(s):  
Analytic Function ◽  
Convex Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Integral Means ◽  
Area Measure ◽  
Area Integral

AbstractFor an analytic function ऒ on the unit disk , we show that the L2 integral mean of ऒ on c < |z| < r with respect to the weighted area measure (1 − |z|2)αd A(z) is a logarithmically convex function of r on (c, 1), where −3 ≤ ∞ ≤ 0 and c ∈ [0, 1). Moreover, the range [−3, 0] for ∞ is best possible. When c = 0, our arguments here also simplify the proof for several results we obtained in earlier papers.

scholarly journals LOGARITHMIC CONVEXITY OF AREA INTEGRAL MEANS FOR ANALYTIC FUNCTIONS II

2014 ◽  
Vol 98 (1) ◽  
pp. 117-128 ◽  
Author(s):  
CHUNJIE WANG ◽  
JIE XIAO ◽  
KEHE ZHU
Keyword(s):  
Analytic Function ◽  
Convex Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Integral Means ◽  
Area Measure ◽  
Logarithmic Convexity ◽  
Area Integral

AbstractFor$0<p<\infty$and$-2\leq {\it\alpha}\leq 0$we show that the$L^{p}$integral mean on$r\mathbb{D}$of an analytic function in the unit disk$\mathbb{D}$with respect to the weighted area measure$(1-|z|^{2})^{{\it\alpha}}\,dA(z)$is a logarithmically convex function of$r$on$(0,1)$.

scholarly journals Logarithmic Convexity of Area Integral Means for Analytic Functions

2014 ◽  
Vol 114 (1) ◽  
pp. 149 ◽  
Author(s):  
Chunjie Wang ◽  
Kehe Zhu
Keyword(s):  
Analytic Function ◽  
Convex Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Integral Means ◽  
Area Measure ◽  
Logarithmic Convexity ◽  
Area Integral

We show that the $L^2$ integral mean on $r\mathsf{D}$ of an analytic function in the unit disk $\mathsf{D}$ with respect to the weighted area measure $(1-|z|^2)^\alpha\,dA(z)$, where $-3\le\alpha\le0$, is a logarithmically convex function of $r$ on $(0,1)$. We also show that the range $[-3,0]$ for $\alpha$ is best possible.

Some properties for certain subclasses of analytic functions defined by a general differential operator

2019 ◽  
Vol 13 (07) ◽  
pp. 2050134
Author(s):  
Erhan Deniz ◽  
Murat Çağlar ◽  
Yücel Özkan
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Partial Sums ◽  
Integral Means

In this paper, we study two new subclasses [Formula: see text] and [Formula: see text] of analytic functions which are defined by means of a differential operator. Some results connected to partial sums and neighborhoods and integral means related to these subclasses are obtained.

Integral means of certain analytic functions for fractional calculus

2007 ◽  
Vol 187 (1) ◽  
pp. 425-432 ◽  
Author(s):  
Tadayuki Sekine ◽  
Shigeyoshi Owa ◽  
Kazuyuki Tsurumi
Keyword(s):  
Fractional Calculus ◽  
Analytic Functions ◽  
Integral Means

scholarly journals Maximal Area Integral Problem for Certain Class of Univalent Analytic Functions

2015 ◽  
Vol 13 (2) ◽  
pp. 607-623 ◽  
Author(s):  
Saminathan Ponnusamy ◽  
Swadesh Kumar Sahoo ◽  
Navneet Lal Sharma
Keyword(s):  
Analytic Functions ◽  
Area Integral ◽  
Integral Problem ◽  
Maximal Area

scholarly journals A New Class of Analytic Functions Defined by Using Salagean Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
R. M. El-Ashwah ◽  
M. K. Aouf ◽  
A. A. M. Hassan ◽  
A. H. Hassan
Keyword(s):  
Analytic Functions ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Partial Sums ◽  
Coefficient Estimates ◽  
Integral Means ◽  
New Class ◽  
Sălăgean Operator ◽  
Salagean Operator ◽  
Fractional Calculus Operators

We derive some results for a new class of analytic functions defined by using Salagean operator. We give some properties of functions in this class and obtain numerous sharp results including for example, coefficient estimates, distortion theorem, radii of star-likeness, convexity, close-to-convexity, extreme points, integral means inequalities, and partial sums of functions belonging to this class. Finally, we give an application involving certain fractional calculus operators that are also considered.

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