Analytic functions possessing a positive real part

1948 ◽  
Vol 15 (4) ◽  
pp. 1033-1042 ◽  
Author(s):  
Zeev Nehari
Keyword(s):  
Analytic Functions ◽  
Positive Real Part ◽  
Positive Real

Coefficient Estimates of Some Classes of Analytic Functions

1983 ◽  
Vol 26 (2) ◽  
pp. 202-208
Author(s):  
Nicolas Samaris
Keyword(s):  
Analytic Functions ◽  
Positive Real Part ◽  
Coefficient Estimates ◽  
Positive Real ◽  
Real Functions ◽  
Typically Real ◽  
Typically Real Functions

AbstractWe are concerned with coefficient estimates, and other similar problems, of the typically real functions and of the functions with positive real part. Following the stream of ideas in [1], new results and generalizations of others given in [1], [2] and [3] are obtained.

scholarly journals The Extreme and Support Points of a New Class of Analytic Functions with Positive Real Part

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Zhigang Peng
Keyword(s):  
Analytic Functions ◽  
Extreme Points ◽  
Positive Real Part ◽  
Positive Real ◽  
New Class ◽  
Support Points

Suppose that 0<α<β<+∞. Let 𝒫(α,β) denote the set of functions p(z) that are analytic in D= {z:|z|<1}  and satisfy Rep(z)>0(|z|<1) and α≤p(0)≤β. In this paper, we investigate the extreme points and support points of 𝒫(α,β).

scholarly journals Some characteristic properties of analytic functions

2016 ◽  
Vol 24 (1) ◽  
pp. 353-369
Author(s):  
R. K. Raina ◽  
Poonam Sharma ◽  
G. S. Sălăgean
Keyword(s):  
Convex Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Positive Real Part ◽  
Integral Representations ◽  
Open Unit ◽  
Open Unit Disk ◽  
Positive Real ◽  
Bilinear Mapping ◽  
Initial Coefficient

AbstractIn this paper, we consider a class L(λ, μ; ϕ) of analytic functions f defined in the open unit disk U satisfying the subordination condition that,where is the Sălăgean operator and ϕ(z) is a convex function with positive real part in U. We obtain some characteristic properties giving the coefficient inequality, radius and subordination results, and an inclusion result for the above class when the function ϕ(z) is a bilinear mapping in the open unit disk. For these functions f (z) ; sharp bounds for the initial coefficient and for the Fekete-Szegö functional are determined, and also some integral representations are given.

scholarly journals Generalizing Certain Analytic Functions Correlative to the n-th Coefficient of Certain Class of Bi-Univalent Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Hameed Ur Rehman ◽  
Maslina Darus ◽  
Jamal Salah
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Positive Real Part ◽  
Polynomial Expansion ◽  
Open Unit ◽  
Open Unit Disk ◽  
Positive Real ◽  
Faber Polynomial ◽  
Coefficient Problems

In the present paper, the authors implement the two analytic functions with its positive real part in the open unit disk. New types of polynomials are introduced, and by using these polynomials with the Faber polynomial expansion, a formula is structured to solve certain coefficient problems. This formula is applied to a certain class of bi-univalent functions and solve the n -th term of its coefficient problems. In the last section of the article, several well-known classes are also extended to its n -th term.

scholarly journals On Mean Distortion for Analytic Functions with Positive Real Part in a Circle

1967 ◽  
Vol 29 ◽  
pp. 221-228
Author(s):  
Yûsaku Komatu
Keyword(s):  
Unit Circle ◽  
Analytic Functions ◽  
Positive Real Part ◽  
Classical Theorem ◽  
Positive Real ◽  
Distortion Theorems

Let be the class of analytic functions Ф(z) which are regular and of positive real part in the unit circle | z | <1 and normalized by Ф(0) = 1. Several distortion theorems have been obtained on various functionals in this class. In a previous paper [4] we have dealt with mean distortion which generalizes a classical theorem of Rogosinski [6].

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