Starlikeness and convexity of the product of certain multivalent functions with higher-order derivatives

2021 ◽  
Vol 71 (2) ◽  
pp. 331-340
Author(s):  
Mohamed K. Aouf ◽  
Abdel Moneim Lashin ◽  
Teodor Bulboacă
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Integral Operators ◽  
Higher Order ◽  
Positive Order ◽  
Starlike And Convex Functions

Abstract In this paper we introduce some new subclasses of the p-valent analytic functions with higher-order derivatives that generalize some related subclasses of starlike and convex functions of a positive order. We found the order of (p,q)-valent starlikeness and convexity for the products of functions that belong to these classes. The order of (p,q)-valent starlikeness and convexity of certain integral operators for the product of functions of these classes were also obtained.

Majorization of starlike and convex functions of complex order involving linear operators

2016 ◽  
Vol 66 (1) ◽  
Author(s):  
G. Murugusundaramoorthy ◽  
K. Thilagavathi
Keyword(s):  
Linear Operator ◽  
Convex Functions ◽  
Analytic Functions ◽  
Linear Operators ◽  
Starlike And Convex Functions ◽  
Complex Order

AbstractThe main object of this present paper is to investigate the problem of majorization of certain class of analytic functions of complex order defined by the Dziok-Raina linear operator. Moreover we point out some new or known consequences of our main result.

scholarly journals Fekete–Szegö problem for certain subclasses of analytic functions

2012 ◽  
Vol 45 (4) ◽  
Author(s):  
Halit Orhan ◽  
Erhan Deniz ◽  
Murat Çağlar
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Starlike And Convex Functions ◽  
Complex Order

AbstractIn this present investigation, authors introduce certain subclasses of starlike and convex functions of complex order

scholarly journals Starlikeness of Functions Defined by Third-Order Differential Inequalities and Integral Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
R. Chandrashekar ◽  
Rosihan M. Ali ◽  
K. G. Subramanian ◽  
A. Swaminathan
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disk ◽  
Differential Inequalities ◽  
Third Order ◽  
Positive Order

Sufficient conditions are obtained to ensure starlikeness of positive order for analytic functions defined in the open unit disk satisfying certain third-order differential inequalities. As a consequence, conditions for starlikeness of functions defined by integral operators are obtained. Connections are also made to earlier known results.

scholarly journals Note on Neighborhoods of Some Classes of Analytic Functions with Negative Coefficients

2011 ◽  
Vol 2011 ◽  
pp. 1-7
Author(s):  
Irina Dorca ◽  
Mugur Acu ◽  
Daniel Breaz
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Starlike And Convex Functions ◽  
Inclusion Relations

In this paper, we prove several inclusion relations associated with the (n,δ) neighborhoods of some subclasses of starlike and convex functions with negative coefficients.

scholarly journals On subclasses of close-to-convex functions of higher order

1992 ◽  
Vol 15 (2) ◽  
pp. 279-289 ◽  
Author(s):  
Khalida Inayat Noor
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Higher Order ◽  
Arc Length ◽  
Covering Theorem ◽  
Bounded Boundary Rotation ◽  
Boundary Rotation

The classesTk(ρ),0≤ρ<1,k≥2, of analytic functions, using the classVk(ρ)of functions of bounded boundary rotation, are defined and it is shown that the functions in these classes are close-to-convex of higher order. Covering theorem, arc-length result and some radii problems are solved. We also discuss some properties of the classVk(ρ)including distortion and coefficient results.

scholarly journals Classes of uniformly starlike and convex functions

2004 ◽  
Vol 2004 (55) ◽  
pp. 2959-2961 ◽  
Author(s):  
Saeid Shams ◽  
S. R. Kulkarni ◽  
Jay M. Jahangiri
Keyword(s):  
Convex Functions ◽  
Integral Operators ◽  
Geometrical Properties ◽  
Starlike And Convex Functions ◽  
Uniformly Starlike

Some classes of uniformly starlike and convex functions are introduced. The geometrical properties of these classes and their behavior under certain integral operators are investigated.

scholarly journals Study on new integral operators defined using confluent hypergeometric function

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Georgia Irina Oros
Keyword(s):  
Hypergeometric Function ◽  
Complex Plane ◽  
Convex Functions ◽  
Univalent Functions ◽  
Integral Operators ◽  
Confluent Hypergeometric Function ◽  
Differential Inequalities ◽  
Starlike And Convex Functions ◽  
Inclusion Properties ◽  
Admissible Functions

AbstractTwo new integral operators are defined in this paper using the classical Bernardi and Libera integral operators and the confluent (or Kummer) hypergeometric function. It is proved that the new operators preserve certain classes of univalent functions, such as classes of starlike and convex functions, and that they extend starlikeness of order $\frac{1}{2}$ 1 2 and convexity of order $\frac{1}{2}$ 1 2 to starlikeness and convexity, respectively. For obtaining the original results, the method of admissible functions is used, and the results are also written as differential inequalities and interpreted using inclusion properties for certain subsets of the complex plane. The example provided shows an application of the original results.

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 On Starlike and Convex Functions with Respect to -Symmetric Points

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Afaf A. Ali Abubaker ◽  
Maslina Darus
Keyword(s):  
Differential Operator ◽  
Convex Functions ◽  
Analytic Functions ◽  
Starlike And Convex Functions ◽  
Symmetric Points

We introduce new subclasses and of analytic functions with respect to -symmetric points defined by differential operator. Some interesting properties for these classes are obtained.

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