scholarly journals A distortion theorem of univalent functions related to symmetric three points

1962 ◽  
Vol 14 (1) ◽  
pp. 26-30 ◽  
Author(s):  
Nobuyuki Suita
Keyword(s):  
Univalent Functions ◽  
Distortion Theorem

Application of fractional calculus operators for a new class of univalent functions with negative coefficients defined by Hohlov operator

2010 ◽  
Vol 60 (1) ◽  
Author(s):  
Waggas Atshan
Keyword(s):  
Fractional Calculus ◽  
Unit Disc ◽  
Univalent Functions ◽  
Distortion Theorem ◽  
New Class ◽  
Fractional Calculus Operators ◽  
Coefficient Inequalities ◽  
Analytic And Univalent Functions

AbstractIn this paper, we introduce a new class W(a, b, c, γ, β) which consists of analytic and univalent functions with negative coefficients in the unit disc defined by Hohlov operator, we obtain distortion theorem using fractional calculus techniques for this class. Also coefficient inequalities and some results for this class are obtained.

scholarly journals Certain classes of univalent functions with negative coefficients II

1976 ◽  
Vol 15 (3) ◽  
pp. 467-473 ◽  
Author(s):  
V.P. Gupta ◽  
P.K. Jain
Keyword(s):  
Univalent Functions ◽  
Arithmetic Mean ◽  
Distortion Theorem ◽  
Linear Combinations ◽  
Radius Of Convexity ◽  
Image Position ◽  
Class Of Functions

Let P*(α, β) denote the class of functionsanalytic and univalent in |z| < 1 for whichwhere α є [0, 1), β є (0, 1].Sharp results concerning coefficients, distortion theorem and radius of convexity for the class P*(α, β) are determined. A comparable theorem for the classes C*(α, β) and P*(α, β) is also obtained. Furthermore, it is shown that the class P*(α, ß) is closed under ‘arithmetic mean’ and ‘convex linear combinations’.

scholarly journals MEROMORPHIC UNIVALENT FUNCTIONS WITH NEGATIVE COEFFICIENTS

1996 ◽  
Vol 27 (1) ◽  
pp. 81-88
Author(s):  
S. M. SARANGI ◽  
SUGUNA B. URALEGADDI
Keyword(s):  
Univalent Functions ◽  
Extreme Points ◽  
Integral Operators ◽  
Starlike Functions ◽  
Distortion Theorem ◽  
Coefficient Inequalities ◽  
Meromorphic Univalent Functions

Coefficient inequalities, distortion theorem, extreme points and prop­ erty preserving integral operators are obtained for certam subclasses of meromor­phic starlike functions with negative coefficints. Convolutions of functions in these classes are also obtained.

scholarly journals On Harmonic Functions Defined by Differential Operator with Respect tok-Symmetric Points

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Afaf A. Ali Abubaker ◽  
Maslina Darus
Keyword(s):  
Differential Operator ◽  
Representation Theorem ◽  
Harmonic Functions ◽  
Univalent Functions ◽  
Distortion Theorem ◽  
Coefficient Condition ◽  
Symmetric Points

We introduce new classesMHkσ,s(λ,δ,α)andM¯Hkσ,s(λ,δ,α)of harmonic univalent functions with respect tok-symmetric points defined by differential operator. We determine a sufficient coefficient condition, representation theorem, and distortion theorem.

scholarly journals A Class of k-Symmetric Harmonic Functions Involving a Certain q-Derivative Operator

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1812
Author(s):  
Hari M. Srivastava ◽  
Nazar Khan ◽  
Shahid Khan ◽  
Qazi Zahoor Ahmad ◽  
Bilal Khan
Keyword(s):  
Harmonic Functions ◽  
Univalent Functions ◽  
Function Class ◽  
Distortion Theorem ◽  
Additional Parameter ◽  
Sufficient Condition ◽  
Closure Properties ◽  
Derivative Operator ◽  
New Class ◽  
Symmetric Points

In this paper, we introduce a new class of harmonic univalent functions with respect to k-symmetric points by using a newly-defined q-analog of the derivative operator for complex harmonic functions. For this harmonic univalent function class, we derive a sufficient condition, a representation theorem, and a distortion theorem. We also apply a generalized q-Bernardi–Libera–Livingston integral operator to examine the closure properties and coefficient bounds. Furthermore, we highlight some known consequences of our main results. In the concluding part of the article, we have finally reiterated the well-demonstrated fact that the results presented in this article can easily be rewritten as the so-called (p,q)-variations by making some straightforward simplifications, and it will be an inconsequential exercise, simply because the additional parameter p is obviously unnecessary.

Means and coefficients of functions which omit a sequence of values

1977 ◽  
Vol 81 (1) ◽  
pp. 47-57
Author(s):  
Albert Baernstein ◽  
Richard Rochberg
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Maximum Modulus ◽  
Distortion Theorem ◽  
Principle Of Subordination ◽  
Image Position ◽  
Simply Connected

Suppose that f is analytic in the unit disk D. If its range f(D) is contained in a simply connected proper subdomain of the plane, then the principle of subordination and the distortion theorem for univalent functions show thatwhere M(r, f) denotes the maximum modulus of f. Cartwright (2) studied functions which, instead of omitting all values on a continuum stretching to infinity, omit only a sequence of values. She assumed that the sequence {wn} satisfiesandand proved that if f(D) contains none of the points {wn} thenmfor every ε > 0. Cartwright's proof was based on the Ahlfors Distortion Theorem, and is quite complicated. A much simpler proof was given by Pommerenke in (10). The key idea in his proof will also be used in the present paper.

scholarly journals Some Geometric Properties for an Extended Class Involving Holomorphic Functions Defined by Fractional Calculus

2020 ◽  
pp. 1136-1145
Author(s):  
Sattar Kamil Hussein ◽  
Kassim Abdulhameed Jassim
Keyword(s):  
Fractional Calculus ◽  
Unit Disk ◽  
Fractional Derivatives ◽  
Hadamard Product ◽  
Univalent Functions ◽  
Holomorphic Functions ◽  
Distortion Theorem ◽  
Fractional Integrals ◽  
Open Unit ◽  
Open Unit Disk

The main objective of" this paper is to study a subclass of holomrphic and univalent functions with negative coefficients in the open unit disk U= defined by Hadamard Product. We obtain coefficients estimates, distortion theorem , fractional derivatives, fractional integrals, and some results.

scholarly journals A Certain Subclass of Analytic and Univalent Functions Defined by Hadamard Product

2019 ◽  
pp. 87-99
Author(s):  
Dhirgam Allawy Hussein ◽  
Sahar Jaafar Mahmood
Keyword(s):  
Hadamard Product ◽  
Univalent Functions ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Radius Of Starlikeness ◽  
Closure Theorems ◽  
Analytic And Univalent Functions

In this paper, we present a new subclass AD(l, g, a, b) of analytic univalent functions in the open unit disk U. We establish some interesting properties like, coefficient estimates, closure theorems, extreme points, growth and distortion theorem and radius of starlikeness and convexity.

scholarly journals Subclass of harmonic univalent functions associated with Salagean derivative

Filomat ◽  
2009 ◽  
Vol 23 (3) ◽  
pp. 303-309 ◽  
Author(s):  
Sayali Joshi
Keyword(s):  
Univalent Functions ◽  
Distortion Theorem ◽  
Derivative Operator ◽  
Coefficient Bound

In the present paper a new subclass of Harmonic univalent functions is defined using Salegaon derivative operator and several interesting properties like coefficient bound, distortion theorem are obtained.

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