scholarly journals Convexities of Gaussian integral means and weighted integral means for analytic functions

2018 ◽  
Vol 69 (2) ◽  
pp. 525-543 ◽  
Author(s):  
Haiying Li ◽  
Taotao Liu
Keyword(s):  
Analytic Functions ◽  
Integral Means ◽  
Weighted Integral ◽  
Gaussian Integral

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 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.

scholarly journals Integral means of certain class of analytic functions

1993 ◽  
Vol 16 (3) ◽  
pp. 459-464
Author(s):  
Gao Chunyi
Keyword(s):  
Analytic Functions ◽  
Starlike Function ◽  
Integral Means ◽  
Alpha Beta ◽  
Class Of Functions ◽  
Extremal Properties

In this paper we discuss the following class of functionsSλ(α,β)={f(z):|f(z)g(z)−1|<β|λf(z)g(z)+1|,z∈D}  where  0≤λ≤1,0<β≤1,0≤α<1, andf(z)=z+∑n=2∞anznis analytic inD={z:|z|<1},g(z)is a starlike function of orderα. A subordination about this class is obtained, the integral means of functions inSλ(α,β)and some extremal properties are studied.

scholarly journals A subordination results for a class of analytic functions defined by q-differential operator

2020 ◽  
Vol 19 (1) ◽  
pp. 53-64 ◽  
Author(s):  
Basem Aref Frasin ◽  
Gangadharan Murugusundaramoorthy
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Integral Means

AbstractIn this paper, we derive several subordination results and integral means result for certain class of analytic functions defined by means of q-differential operator. Some interesting corollaries and consequences of our results are also considered.

scholarly journals Subordination results for a class of analytic functions

2021 ◽  
Vol 7 (1) ◽  
pp. 30-42
Author(s):  
M. K. Aouf ◽  
B. A. Frasin ◽  
G. Murugusundaramoorthy
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Integral Means ◽  
Complex Order

AbstractIn this paper, we derive several subordination results and integral means result for certain class of analytic functions with complex order defined by means of q-differential operator. Some interesting corollaries and consequences of our results are also considered

scholarly journals On some weighted integral inequalities for convex functions related to Fejér’s result

Filomat ◽  
2011 ◽  
Vol 25 (1) ◽  
pp. 195-218
Author(s):  
K.L. Tseng ◽  
Shiow-Ru Hwang ◽  
S.S. Dragomir
Keyword(s):  
Convex Functions ◽  
Integral Inequalities ◽  
Integral Means ◽  
Weighted Integral

In this paper, we introduce some functionals associated with weighted integral means for convex functions. Some new Fej?r-type inequalities are obtained as well.

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.

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