scholarly journals Coefficient, distortion and growth inequalities for certain p-valent close-to-convex functions

2013 ◽  
Vol 9 (2) ◽  
pp. 57-62
Author(s):  
I.B. Bapana ◽  
Sneha Handwana
Keyword(s):  
Unit Disk ◽  
Convex Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Distortion Theorems

Abstract In the present paper, we introduce and investigate a new subclass χtp(γ) of analytic and p-valent close-to-convex functions in the open unit disk U. For functions belonging to the class χtp(γ), some interesting properties including the coefficient estimates, distortion theorems and subordination results are obtained

scholarly journals Coefficient Estimates of Bi-Starlike and Bi-Convex Functions with Respect to Symmetrical Points Associated with the Second Kind Chebyshev Polynomials

2020 ◽  
pp. 191-198
Author(s):  
Abbas Kareem Wanas
Keyword(s):  
Unit Disk ◽  
Chebyshev Polynomials ◽  
Convex Functions ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Symmetrical Points

In this paper, by making use the second kind Chebyshev polynomials, we introduce and study a certain class of bi-starlike and bi-convex functions with respect to symmetrical points defined in the open unit disk. We find upper bounds for the second and third coefficients of functions belong to this class.

scholarly journals On Subclass of -Uniformly Convex Functions of Complex Order Involving Multiplier Transformations

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Waggas Galib Atshan ◽  
Ali Hamza Abada
Keyword(s):  
Unit Disk ◽  
Convex Functions ◽  
Extreme Points ◽  
Open Unit ◽  
Open Unit Disk ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Integral Means ◽  
Uniformly Convex Functions ◽  
Complex Order

We introduce a subclass of -uniformly convex functions of order with negative coefficients by using the multiplier transformations in the open unit disk . We obtain coefficient estimates, radii of convexity and close-to-convexity, extreme points, and integral means inequalities for the function that belongs to the class .

scholarly journals CERTAIN CLASSES OF ANALYTIC AND MULTIVALENT FUNCTIONS

1998 ◽  
Vol 29 (3) ◽  
pp. 233-244
Author(s):  
H. M. ROSSEN ◽  
H. M. SRIVASTAVA ◽  
M. K. AOUF
Keyword(s):  
Unit Disk ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Distortion Theorems ◽  
Growth And Distortion Theorems ◽  
Special Classes

The main object of the present paper is to investigate the special classes \[\mathcal P_\alpha^*(p, A, B) \text { and } \mathcal R_\alpha^*(p, A, B) \] \[(0\le \alpha<p; -a\le B<A\le 1; p\in\mathbb{N})\] of analytic and $p$-valent functions in the open unit disk $U$. In particular, various growth and distortion theorems, and several coefficient estimates, are obtained for these as well as related classes of analytic and $p$-valent functions in $\mathcal U$.

Coefficient Estimates for Certain Subclasses of m-Fold Symmetric Bi-univalent Functions Associated with Pseudo-Starlike Functions

2021 ◽  
pp. 209-223
Author(s):  
Timilehin G. Shaba ◽  
Amol B. Patil
Keyword(s):  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Starlike Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

In the present investigation, we introduce the subclasses $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\phi)$ and $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\delta)$ of \textit{m}-fold symmetric bi-univalent function class $\Sigma_m$, which are associated with the pseudo-starlike functions and defined in the open unit disk $\mathbb{U}$. Moreover, we obtain estimates on the initial coefficients $|b_{m+1}|$ and $|b_{2m+1}|$ for the functions belong to these subclasses and identified correlations with some of the earlier known classes.

scholarly journals On Certain Classes of Convex Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Young Jae Sim ◽  
Oh Sang Kwon
Keyword(s):  
Unit Disk ◽  
Convex Functions ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Real Numbers ◽  
Inverse Functions

For real numbersαandβsuch that0≤α<1<β, we denote by𝒦α,βthe class of normalized analytic functions which satisfy the following two sided-inequality:α<ℜ1+zf′′z/f′z<β  z∈𝕌,where𝕌denotes the open unit disk. We find some relationships involving functions in the class𝒦(α,β). And we estimate the bounds of coefficients and solve the Fekete-Szegö problem for functions in this class. Furthermore, we investigate the bounds of initial coefficients of inverse functions or biunivalent functions.

scholarly journals Coefficient Estimates for a Subclass of Analytic Functions Associated with a Certain Leaf-Like Domain

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1334
Author(s):  
Bilal Khan ◽  
Hari M. Srivastava ◽  
Nazar Khan ◽  
Maslina Darus ◽  
Muhammad Tahir ◽  
...  
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Second Order ◽  
Open Unit ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Coefficient Estimates ◽  
Principle Of Subordination

First, by making use of the concept of basic (or q-) calculus, as well as the principle of subordination between analytic functions, generalization Rq(h) of the class R(h) of analytic functions, which are associated with the leaf-like domain in the open unit disk U, is given. Then, the coefficient estimates, the Fekete–Szegö problem, and the second-order Hankel determinant H2(1) for functions belonging to this class Rq(h) are investigated. Furthermore, similar results are examined and presented for the functions zf(z) and f−1(z). For the validity of our results, relevant connections with those in earlier works are also pointed out.

scholarly journals Some Connections between Class𝒰- andα-Convex Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Edmond Aliaga ◽  
Nikola Tuneski
Keyword(s):  
Convex Function ◽  
Unit Disk ◽  
Convex Functions ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk

The class𝒰(λ,μ)of normalized analytic functions that satisfy|(z/f(z))1+μ·f′(z)−1|<λfor allzin the open unit disk is studied and sufficient conditions for anα-convex function to be in𝒰(λ,μ)are given.

Coefficient Estimates and Quasi-Subordination Properties Associated with Certain Subclasses of Analytic and Bi-Univalent Functions

2015 ◽  
Vol 65 (3) ◽  
Author(s):  
S. P. Goyal ◽  
Rakesh Kumar
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

AbstractIn the present paper, we obtain the estimates on initial coefficients of normalized analytic function f in the open unit disk with f and its inverse g = f

scholarly journals Properties of certainp-valently convex functions

2003 ◽  
Vol 2003 (41) ◽  
pp. 2603-2608 ◽  
Author(s):  
Dinggong Yang ◽  
Shigeyoshi Owa
Keyword(s):  
Unit Disk ◽  
Convex Functions ◽  
Open Unit ◽  
Open Unit Disk

A subclass𝒞p(λ,μ)(p∈ℕ, 0<λ<1, −λ≦μ<1)ofp-valently convex functions in the open unit disk𝕌is introduced. The object of the present paper is to discuss some interesting properties of functions belonging to the class𝒞p(λ,μ).

scholarly journals On the second hankel determinant for the kth-root transform of analytic functions

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 227-245 ◽  
Author(s):  
Najla Alarifi ◽  
Rosihan Ali ◽  
V. Ravichandran
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Convex Functions ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Second Hankel Determinant ◽  
The Given ◽  
Logarithmically Convex Functions

Let f be a normalized analytic function in the open unit disk of the complex plane satisfying zf'(z)/f(z) is subordinate to a given analytic function ?. A sharp bound is obtained for the second Hankel determinant of the kth-root transform z[f(zk)/zk]1/k. Best bounds for the Hankel determinant are also derived for the kth-root transform of several other classes, which include the class of ?-convex functions and ?-logarithmically convex functions. These bounds are expressed in terms of the coefficients of the given function ?, and thus connect with earlier known results for particular choices of ?.

Sign in / Sign up

Export Citation Format

Share Document