Extreme points of families of analytic functions subordinate to convex mappings

1981 ◽  
Vol 176 (4) ◽  
pp. 511-519 ◽  
Author(s):  
Yusuf Abu-Muhanna ◽  
Thomas H. MacGregor
Keyword(s):  
Analytic Functions ◽  
Extreme Points ◽  
Convex Mappings

scholarly journals Class of Analytic Function Related with Uniformly Convex and Janowski’s Functions

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Akhter Rasheed ◽  
Saqib Hussain ◽  
Muhammad Asad Zaighum ◽  
Maslina Darus
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Unit Disc ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Open Unit ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Open Unit Disc

In this paper, we introduce a new subclass of analytic functions in open unit disc. We obtain coefficient estimates, extreme points, and distortion theorem. We also derived the radii of close-to-convexity and starlikeness for this class.

scholarly journals EXTREME POINTS OF INTEGRAL FAMILIES OF ANALYTIC FUNCTIONS

2013 ◽  
Vol 94 (2) ◽  
pp. 202-221
Author(s):  
KEIKO DOW ◽  
D. R. WILKEN
Keyword(s):  
Analytic Functions ◽  
Compact Convex ◽  
Extreme Points ◽  
Starlike Functions ◽  
Extremal Problems ◽  
Kernel Functions ◽  
Closed Convex Hull ◽  
New Class ◽  
Geometric Function ◽  
Derivatives Of

AbstractExtreme points of compact, convex integral families of analytic functions are investigated. Knowledge about extreme points provides a valuable tool in the optimization of linear extremal problems. The functions studied are determined by a two-parameter collection of kernel functions integrated against measures on the torus. For specific choices of the parameters many families from classical geometric function theory are included. These families include the closed convex hull of the derivatives of normalized close-to-convex functions, the ratio of starlike functions of different orders, as well as many others. The main result introduces a surprising new class of extreme points.

scholarly journals The Extreme and Support Points of a New Class of Analytic Functions with Positive Real Part

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Zhigang Peng
Keyword(s):  
Analytic Functions ◽  
Extreme Points ◽  
Positive Real Part ◽  
Positive Real ◽  
New Class ◽  
Support Points

Suppose that 0<α<β<+∞. Let 𝒫(α,β) denote the set of functions p(z) that are analytic in D= {z:|z|<1}  and satisfy Rep(z)>0(|z|<1) and α≤p(0)≤β. In this paper, we investigate the extreme points and support points of 𝒫(α,β).

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 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 Non-extreme-Points Approach to Extreme Points of Integral Families of Analytic Functions

10.53733/87 ◽  
2021 ◽  
Vol 51 ◽  
pp. 39-48
Author(s):  
Keiko Dow
Keyword(s):  
Unit Circle ◽  
Extreme Point ◽  
Analytic Functions ◽  
Compact Convex ◽  
Extreme Points ◽  
Starlike Functions ◽  
Extremal Problems ◽  
Kernel Functions ◽  
Closed Convex Hull ◽  
Special Cases

Non extreme points of compact, convex integral families of analytic functions are investigated. Knowledge about extreme points provides a valuable tool in the optimization of linear extremal problems. The functions studied are determined by a 2-parameter collection of kernel functions integrated against measures on the torus. Families from classical geometric function theory such as the closed convex hull of the derivatives of normalized close-to-convex functions, the ratio of starlike functions of different orders, as well as many others are included. However for these families of analytic functions, identifying “all” the extreme points remains a difficult challenge except in some special cases. Aharonov and Friedland [1] identified a band of points on the unit circle which corresponds to the set of extreme points for these 2-parameter collections of kernel functions. Later this band of extreme points was further extended by introducing a new technique by Dow and Wilken [3]. On the other hand, a technique to identify a non extreme point was not investigated much in the past probably because identifying non extreme points does not directly help solving the optimization of linear extremal problems. So far only one point on the unit circle has beenidentified which corresponds to a non extreme point for a 2-parameter collections of kernel functions. This leaves a big gap between the band of extreme points and one non extreme point. The author believes it is worth developing some techniques, and identifying non extreme points will shed a new light in the exact determination of the extreme points. The ultimate goal is to identify the point on the unit circle that separates the band of extreme points from non extreme points. The main result introduces a new class of non extreme points.

scholarly journals Study on Certain Subclass of Analytic Functions Involving Mittag-Leffler Function

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Nazek Alessa ◽  
B. Venkateswarlu ◽  
K. Loganathan ◽  
P. Thirupathi Reddy ◽  
A. Shashikala ◽  
...  
Keyword(s):  
Analytic Functions ◽  
Extreme Points ◽  
Partial Sums ◽  
Derivative Operator ◽  
Regular Functions

We propose and explore a new subclass of regular functions described by a new derivative operator in this paper. Some coefficient estimations, growth and distortion aspects, extreme points, star-like radii, convexity, Fekete-Szego inequality, and partial sums are derived.

scholarly journals A Certain Subclass of Multivalent Analytic Functions with Negative Coefficients for Operator on Hilbert Space

2019 ◽  
pp. 355-364
Author(s):  
Asraa Abdul Jaleel Husien
Keyword(s):  
Hilbert Space ◽  
Analytic Functions ◽  
Convex Set ◽  
Extreme Points ◽  
Complex Hilbert Space ◽  
Coefficient Estimates ◽  
Geometric Properties

In the present work, we introduce and study a certain subclass for multivalent analytic functions with negative coefficients defined on complex Hilbert space. We establish a number of geometric properties, like, coefficient estimates, convex set, extreme points and radii of starlikeness and convexity.

scholarly journals New Family of Multivalent Analytic Functions Defined on Complex Hilbert Space

2020 ◽  
pp. 155-165 ◽  
Author(s):  
Abbas Kareem Wanas ◽  
S. R. Swamy
Keyword(s):  
Hilbert Space ◽  
Analytic Functions ◽  
Convex Set ◽  
Extreme Points ◽  
Complex Hilbert Space ◽  
Coefficient Estimates ◽  
Geometric Properties ◽  
New Class ◽  
New Family

In this article, we define a certain new class of multivalent analytic functions with negative coefficients on complex Hilbert space. We derive a number of important geometric properties, such as, coefficient estimates, radii of starlikeness and convexity, extreme points and convex set.

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