On p-Valently Close-To-Convex and Starlike Functions

1990 ◽  
Vol 147 (1) ◽  
pp. 65-73
Author(s):  
Shigeyoshi Owa
Keyword(s):  
Starlike Functions ◽  
Convex And Starlike Functions

scholarly journals A Subclass of Analytic Functions Related tok-Uniformly Convex and Starlike Functions

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Saqib Hussain ◽  
Akhter Rasheed ◽  
Muhammad Asad Zaighum ◽  
Maslina Darus
Keyword(s):  
Convolution Operator ◽  
Starlike Functions ◽  
Distortion Theorem ◽  
Open Unit ◽  
Uniformly Convex ◽  
Open Unit Disc ◽  
Coefficient Inequalities ◽  
Uniformly Starlike Functions ◽  
Convex And Starlike Functions ◽  
Uniformly Starlike

We investigate some subclasses ofk-uniformly convex andk-uniformly starlike functions in open unit disc, which is generalization of class of convex and starlike functions. Some coefficient inequalities, a distortion theorem, the radii of close-to-convexity, and starlikeness and convexity for these classes of functions are studied. The behavior of these classes under a certain modified convolution operator is also discussed.

scholarly journals Convex and starlike criteria

1999 ◽  
Vol 22 (1) ◽  
pp. 75-79 ◽  
Author(s):  
Herb Silverman
Keyword(s):  
Sufficient Conditions ◽  
Starlike Functions ◽  
Positive Order ◽  
Convex And Starlike Functions

We investigate an expression involving the quotient of the analytic representations of convex and starlike functions. Sufficient conditions are found for functions to be starlike of a positive order and convex.

scholarly journals Multivalent Functions Related with an Integral Operator

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Syed Ghoos Ali Shah ◽  
Saqib Hussain ◽  
Saima Noor ◽  
Maslina Darus ◽  
Ibrar Ahmad
Keyword(s):  
Integral Operator ◽  
Hadamard Product ◽  
Starlike Functions ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Rate Of Growth ◽  
Convex And Starlike Functions

In this present paper, we introduce and explore certain new classes of uniformly convex and starlike functions related to the Liu–Owa integral operator. We explore various properties and characteristics, such as coefficient estimates, rate of growth, distortion result, radii of close-to-convexity, starlikeness, convexity, and Hadamard product. It is important to mention that our results are a generalization of the number of existing results in the literature.

scholarly journals On a class of functions unifying the classes of Paatero, Robertson and others

1988 ◽  
Vol 11 (2) ◽  
pp. 251-258 ◽  
Author(s):  
S. Bhargava ◽  
S. Nanjunda Rao
Keyword(s):  
Variational Principle ◽  
Schwarzian Derivative ◽  
Starlike Functions ◽  
Class A ◽  
Boundary Rotation ◽  
Alpha Beta ◽  
Spirallike Functions ◽  
Convex And Starlike Functions ◽  
Number Of Classes ◽  
Class Of Functions

We study a classMkλ(α,β,b,c)of analytic functions which unifies a number of classes studied previously by Paatero, Robertson, Pinchuk, Moulis, Mocanu and others. Thus our class includes convex and starlike functions of orderβ, spirallike functions of orderβand functions for whichzf′is spirallike of orderβ, functions of boundary rotation utmostkπ,α-convex functions etc. An integral representation of Paatero and a variational principle of Robertson for the classVkof functions of bounded boundary rotation, yield some representation theorems and a variational principle for our class. A consequence of these basic theorems is a theorem for this classMkλ(α,β,b,c)which unifies some earlier results concerning the radii of convexity of functions in the classVkλ(β)of Moulis and those concerning the radii of starlikeness of functions in the classesUkof Pinchuk andU2(β)of Robertson etc. By applying an estimate of Moulis concerning functions inVkλ(0), we obtain an inequality in the classMkλ(α,β,b,c)which will contain an estimate for the Schwarzian derivative of functions in the classVkλ(β)and in particular the estimate of Moulis for the Schwarzian of functions inVkλ(0).

scholarly journals New classes of $k$-uniformly convex and starlike functions

2004 ◽  
Vol 35 (3) ◽  
pp. 261-266 ◽  
Author(s):  
Essam Aqlan ◽  
Jay M. Jahangiri ◽  
S. R. Kulkarni
Keyword(s):  
Analytic Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Uniformly Convex ◽  
Radius Of Starlikeness ◽  
Distortion Bounds ◽  
Convex And Starlike Functions

Certain classes of analytic functions are defined which will generalize new, as well as well-known, classes of k-uniformly convex and starlike functions. We provide necessary and sufficent coefficient conditions, distortion bounds, extreme points and radius of starlikeness for these classes.

SECOND HANKEL DETERMINANT OF LOGARITHMIC COEFFICIENTS OF CONVEX AND STARLIKE FUNCTIONS

2021 ◽  
pp. 1-10
Author(s):  
BOGUMIŁA KOWALCZYK ◽  
ADAM LECKO
Keyword(s):  
Univalent Functions ◽  
Starlike Functions ◽  
Hankel Determinant ◽  
Hankel Matrices ◽  
Sharp Bounds ◽  
Second Hankel Determinant ◽  
Logarithmic Coefficients ◽  
Convex And Starlike Functions

Abstract We begin the study of Hankel matrices whose entries are logarithmic coefficients of univalent functions and give sharp bounds for the second Hankel determinant of logarithmic coefficients of convex and starlike functions.

scholarly journals On the Largest Disc Mapped by Sum of Convex and Starlike Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Rosihan M. Ali ◽  
Naveen Kumar Jain ◽  
V. Ravichandran
Keyword(s):  
Analytic Function ◽  
Half Plane ◽  
Unit Disc ◽  
Starlike Functions ◽  
Positive Real Part ◽  
Positive Real ◽  
Convex And Starlike Functions ◽  
The Right

For a normalized analytic functionfdefined on the unit disc𝔻, letϕ(f,f′,f′′;z)be a function of positive real part in𝔻,ψ(f,f′,f′′;z)need not have that property in𝔻, andχ=ϕ+ψ. For certain choices ofϕandψ, a sharp radius constantρis determined,0<ρ<1, so thatχ(ρz)/ρmaps𝔻onto a specified region in the right half-plane.

Sign in / Sign up

Export Citation Format

Share Document