Extremal problems in the class of functions with bounded boundary rotation of complex order

1994 ◽  
Vol 70 (6) ◽  
pp. 2080-2084
Author(s):  
E. G. Goluzina
Keyword(s):  
Extremal Problems ◽  
Complex Order ◽  
Bounded Boundary Rotation ◽  
Boundary Rotation ◽  
Class Of Functions

scholarly journals On functions of bounded boundary rotation I

1969 ◽  
Vol 16 (4) ◽  
pp. 339-347 ◽  
Author(s):  
D. A. Brannan
Keyword(s):  
Upper Bound ◽  
Convex Functions ◽  
Image Domain ◽  
Basic Properties ◽  
Bounded Boundary Rotation ◽  
Boundary Rotation ◽  
Image Position ◽  
Class Of Functions

Let Vk denote the class of functionswhich map conformally onto an image domain ƒ(U) of boundary rotation at most kπ (see (7) for the definition and basic properties of the class kπ). In this note we discuss the valency of functions in Vk, and also their Maclaurin coefficients.In (8) it was shown that functions in Vk are close-to-convex in . Here we show that Vk is a subclass of the class K(α) of close-to-convex functions of order α (10) for , and we give an upper bound for the valency of functions in Vk for K>4.

Curvature and Radius of Curvature for Functions with Bounded Boundary Rotation

1973 ◽  
Vol 25 (5) ◽  
pp. 1015-1023 ◽  
Author(s):  
J. W. Noonan
Keyword(s):  
Bounded Variation ◽  
Radius Of Curvature ◽  
Function Of Bounded Variation ◽  
Bounded Boundary Rotation ◽  
Boundary Rotation ◽  
Image Position ◽  
Class Of Functions

For k ≧ 2 denote by Vk the class of functions f regular in and having the representation(1.1)where μ is a real-valued function of bounded variation on [0, 2π] with(1.2)Vk is the class of functions with boundary rotation at most kπ.

On Odd Functions of Bounded Boundary Rotation

1974 ◽  
Vol 26 (3) ◽  
pp. 551-564
Author(s):  
Ronald J. Leach
Keyword(s):  
Unit Disc ◽  
Bounded Boundary Rotation ◽  
Boundary Rotation ◽  
Definition Of ◽  
Image Position ◽  
Class Of Functions

Let VK denote the class of functionsthat are analytic in the unit disc U, satisfy f′(z) ≠ 0 in U, and map U onto a domain with boundary rotation at most Kπ (for a definition of this concept, see [9]). V. Paatero [9] showed that f(z) ∊ VK if and only if1.1

scholarly journals On certain classes ofp-Valent functions

1986 ◽  
Vol 9 (1) ◽  
pp. 55-64 ◽  
Author(s):  
M. K. Aouf
Keyword(s):  
Critical Points ◽  
Complex Number ◽  
Bounded Boundary Rotation ◽  
Boundary Rotation ◽  
Class Of Functions

LetVkλ(α,b,p)(k≥2,b≠0is any complex number,0≤α<pand|λ|<π/2) denote the class of functionsf(z)=zp+∑n=p+1∞anznanalytic inU={z:|z|<1}having(p−1)critical points inUand satisfyinglimr→1−sup∫02π|Re{eiλ[p+1b(1+zf″(z)f′(z)−p)]−αcosλ}p−α|dθ≤kπcosλ.In this paper we generalize both those functionsf(z)which arep-valent convex of orderα,0≤α<p, with bounded boundary rotation and thosep-valent functionsf(z)for whichzf′(z)/pisλ-spirallike of orderα,0≤α<p.

Some extremal problems for functions of bounded boundary rotation

1981 ◽  
Vol 39 (1-2) ◽  
pp. 46-62
Author(s):  
Roman Boutellier ◽  
Albert Pfluger
Keyword(s):  
Extremal Problems ◽  
Bounded Boundary Rotation ◽  
Boundary Rotation

Toeplitz matrices whose elements are coefficients of Bazilevič functions

2018 ◽  
Vol 16 (1) ◽  
pp. 1161-1169
Author(s):  
Varadharajan Radhika ◽  
Jay M. Jahangiri ◽  
Srikandan Sivasubramanian ◽  
Gangadharan Murugusundaramoorthy
Keyword(s):  
Convex Functions ◽  
Toeplitz Matrices ◽  
Upper Bounds ◽  
Bounded Boundary Rotation ◽  
Boundary Rotation ◽  
Bazilevic Functions ◽  
Class Of Functions

AbstractWe consider the Toeplitz matrices whose elements are the coefficients of Bazilevič functions and obtain upper bounds for the first four determinants of these Toeplitz matrices. The results presented here are new and noble and the only prior compatible results are the recent publications by Thomas and Halim [1] for the classes of starlike and close-to-convex functions and Radhika et al. [2] for the class of functions with bounded boundary rotation.

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