scholarly journals Certain classes of univalent functions with negative coefficients

1976 ◽  
Vol 14 (3) ◽  
pp. 409-416 ◽  
Author(s):  
V.P. Gupta ◽  
P.K. Jain
Keyword(s):  
Univalent Functions ◽  
Representation Formula ◽  
Arithmetic Mean ◽  
Linear Combinations ◽  
Analytic And Univalent Functions

The subclasses S*(α, β) and C*(α, β) of T, the class of analytic and univalent functions of the form have been considered. Sharp results concerning coefficients, distortion of functions belonging to S*(α, β) and C*(α, β) are determined along with a representation formula for the functions in S*(α, β). Furthermore, it is shown that the classes S*(α, β) and C*(α,.β) are closed under arithmetic mean and convex linear combinations.

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’.

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 New Subclasses concerning Some Analytic and Univalent Functions

2017 ◽  
Vol 2017 ◽  
pp. 1-4
Author(s):  
Maslina Darus ◽  
Shigeyoshi Owa
Keyword(s):  
Unit Disc ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disc ◽  
Analytic And Univalent Functions

Considering a function f(z)=z/1-z2 which is analytic and starlike in the open unit disc U and a function f(z)=z/1-z which is analytic and convex in U, we introduce two new classes Sα⁎(β) and Kα(β) concerning fα(z)=z/1-zα  (α>0). The object of the present paper is to discuss some interesting properties for functions in the classes Sα⁎(β) and Kα(β).

Linear Combinations of Univalent Functions with Complex Coefficients

1971 ◽  
Vol 23 (4) ◽  
pp. 712-717 ◽  
Author(s):  
Robert K. Stump
Keyword(s):  
Linear Combination ◽  
Convex Domain ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Linear Combinations ◽  
Radius Of Starlikeness ◽  
Complex Constant ◽  
Complex Functions ◽  
Image Position ◽  
Complex Coefficients

Let U be the class of all normalized analytic functionswhere z ∈ E = {z : |z| < 1} and ƒ is univalent in E. Let K denote the sub-class of U consisting of those members that map E onto a convex domain. MacGregor [2] showed that if ƒ1 ∈ K and ƒ2 ∈ K and if1then F ∉ K when λ is real and 0 < λ < 1, and the radius of univalency and starlikeness for F is .In this paper, we examine the expression (1) when ƒ1 ∈ K, ƒ2 ∈ K and λ is a complex constant and find the radius of starlikeness for such a linear combination of complex functions with complex coefficients.

scholarly journals Coefficient Inequalities of Functions Associated with Petal Type Domains

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 298 ◽  
Author(s):  
Sarfraz Malik ◽  
Shahid Mahmood ◽  
Mohsan Raza ◽  
Sumbal Farman ◽  
Saira Zainab
Keyword(s):  
Taylor Series ◽  
Upper Bound ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Series Representation ◽  
Functional Inequalities ◽  
Major Interest ◽  
Coefficient Inequalities ◽  
Inverse Functions ◽  
Analytic And Univalent Functions

In the theory of analytic and univalent functions, coefficients of functions’ Taylor series representation and their related functional inequalities are of major interest and how they estimate functions’ growth in their specified domains. One of the important and useful functional inequalities is the Fekete-Szegö inequality. In this work, we aim to analyze the Fekete-Szegö functional and to find its upper bound for certain analytic functions which give parabolic and petal type regions as image domains. Coefficient inequalities and the Fekete-Szegö inequality of inverse functions to these certain analytic functions are also established in this work.

scholarly journals Iterated integral transforms of Caratheodory functions and their applications to analytic and univalent functions

2006 ◽  
Vol 37 (4) ◽  
pp. 355-366
Author(s):  
K. O. Babalola ◽  
T. O. Opoola
Keyword(s):  
Univalent Functions ◽  
Integral Transforms ◽  
Carathéodory Functions ◽  
Iterated Integral ◽  
Analytic And Univalent Functions

In this paper we develop and study some integral transforms of Caratheodory functions. We apply the transforms to study certain other classes of analytic and univalent functions both to obtain new results and provide new proofs of some known ones.

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