Shorter Notes: A Coefficient Inequality for Convex Univalent Functions

1975 ◽  
Vol 48 (1) ◽  
pp. 266 ◽  
Author(s):  
S. Y. Trimble
Keyword(s):  
Univalent Functions ◽  
Coefficient Inequality ◽  
Convex Univalent Functions

scholarly journals Region of Variability for Exponentially Convex Univalent Functions

2010 ◽  
Vol 5 (3) ◽  
pp. 955-966 ◽  
Author(s):  
Ponnusamy Saminathan ◽  
Vasudevarao Allu ◽  
M. Vuorinen
Keyword(s):  
Univalent Functions ◽  
Convex Univalent Functions

scholarly journals Applications of Certain Operators to the Classes of Analytic Functions Related to the Generalized Janowski Functions

2020 ◽  
pp. 211-225
Author(s):  
Khalida Inayat Noor ◽  
Shujaat Ali Shah
Keyword(s):  
Analytic Functions ◽  
Univalent Functions ◽  
Linear Operators ◽  
Janowski Functions ◽  
Radius Problems ◽  
Convex Univalent Functions

We introduce certain subclasses of analytic functions related to the class of analytic, convex univalent functions. We discuss some results including inclusion relationships and invariance of the classes under convex convolution in terms of certain linear operators. Applications of these results associated with the generalized Janowski functions and conic domains are considered. Also, several radius problems are investigated.

UNIVALENCE CONDITIONS FOR A NEW INTEGRAL OPERATOR

2015 ◽  
Vol 1 (2) ◽  
pp. 35-37
Author(s):  
Sh. Najafzadeh ◽  
A. Ebadian ◽  
H. Rahmatan
Keyword(s):  
Integral Operator ◽  
Univalent Functions ◽  
Norm Estimates ◽  
Schwarzian Derivatives ◽  
Convex Univalent Functions

In the present paper, we will obtain norm estimates of the pre-Schwarzian derivatives for $F_{\lambda,\mu}(z)$, such that \[ F_{\lambda,\mu}(z) = \int_0^z \prod_{i=1}^{n} (f'_i(t))^{\lambda_i}\left( \frac{f_i(t)}{t} \right)^{\mu_i}dt \quad (z\in D),\] where $\lambda_i,\mu_i\in \mathbb{R}$, $\lambda_i=(\lambda_1,\lambda_2,\ldots,\lambda_n$, $\mu_i=(\mu_1,\mu_2,\ldots,\mu_n$ and $f_i$ belongs to the class of convex univalent functions $\mathcal{C}\subset \mathcal{S}$.

scholarly journals Quasi-convex univalent functions

1980 ◽  
Vol 3 (2) ◽  
pp. 255-266 ◽  
Author(s):  
K. Inayat Noor ◽  
D. K. Thomas
Keyword(s):  
Univalent Functions ◽  
New Class ◽  
Convex Univalent Functions

In this paper, a new class of normalized univalent functions is introduced. The properties of this class and its relationship with some other subclasses of univalent functions are studied. The functions in this class are close-to-convex.

scholarly journals On Fully-Convex Harmonic Functions and their Extension

2018 ◽  
Vol 38 (2) ◽  
pp. 51-60
Author(s):  
Shahpour Nosrati ◽  
Ahmad Zireh
Keyword(s):  
Harmonic Functions ◽  
Univalent Functions ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Uniformly Convex ◽  
Circular Arc ◽  
Coefficient Condition ◽  
Necessary And Sufficient ◽  
Convex Univalent Functions

‎Uniformly convex univalent functions that introduced by Goodman‎, ‎maps every circular arc contained in the open unit disk with center in it into a convex curve‎. ‎On the other hand‎, ‎a fully-convex harmonic function‎, ‎maps each subdisk $|z|=r<1$ onto a convex curve‎. ‎Here we synthesis these two ideas and introduce a family of univalent harmonic functions which are fully-convex and uniformly convex also‎. ‎In the following we will mention some examples of this subclass and obtain a necessary and sufficient conditions and finally a coefficient condition will attain with convolution‎.

scholarly journals On an integral operator for convex univalent functions

1986 ◽  
Vol 34 (2) ◽  
pp. 211-218
Author(s):  
Vinod Kumar ◽  
S. L. Shukla
Keyword(s):  
Integral Operator ◽  
Real Number ◽  
Complex Number ◽  
Univalent Functions ◽  
Corrected Version ◽  
Convex Univalent Functions ◽  
Class Of Functions

Let K (m,M) denote the class of functions regular and satisfying |1 + zf″(z)/f′(z)− m| < M in |z| < 1, where |m−1| < M ≤ m. Recently, R.K. Pandey and G. P. Bhargava have shown that if f ε K (m,M), then the function du also belongs to K (m,M) provided α is a complex number satisfying the inequality |α| ≤ (1−b)/2, where b = (m-1)/M. In this paper we show by a counterexample that their inequality is in general wrong, and prove a corrected version of their result. We show that F ε K (m,M) provided that α is a real number satisfying −φ ≤ α ≤1, φ = (M−|m−1|)/(M + |m−1|), or a complex number satisfying |α| ≤ φ. In both cases the bounds for α are sharp.

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