On the class of harmonic mappings which is related to the class of bounded boundary rotation

The classVk(p). We generalize the class Vk of analytic functions of bounded boundary rotation [8] by allowing critical points in the unit disc U.Definition. Let f(z) = aqzq + . . . (q 1) be analytic in U. Then f(z) belongs to the class Vk(p) if for r sufficiently close to 1,andWe note that (1.1) implies that / has precisely p — 1 critical points in U.

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Coefficients of Symmetric Functions of Bounded Boundary Rotation

Canadian Journal of Mathematics ◽

10.4153/cjm-1974-128-8 ◽

1974 ◽

Vol 26 (6) ◽

pp. 1351-1355 ◽

Cited By ~ 1

Author(s):

Ronald J. Leach

Keyword(s):

Unit Disc ◽

Symmetric Functions ◽

The Family ◽

Bounded Boundary Rotation ◽

Boundary Rotation ◽

Image Position

Let denote the family of all functions of the formthat are analytic in the unit disc U, f′(z) ≠ 0 in U and f maps U onto a domain of boundary rotation at most . Recently Brannan, Clunie and Kirwan [2] and Aharonov and Friedland [1] have solved the problem of estimating |amp+1| for all , provided m = 1.

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A variational method for functions of bounded boundary rotation

Transactions of the American Mathematical Society ◽

10.1090/s0002-9947-1971-0274737-8 ◽

1971 ◽

Vol 157 ◽

pp. 39-39 ◽

Cited By ~ 4

Author(s):

H. B. Coonce

Keyword(s):

Variational Method ◽

Bounded Boundary Rotation ◽

Boundary Rotation

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Coefficients of symmetric functions of bounded boundary rotation

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-1989-0930244-7 ◽

1989 ◽

Vol 105 (2) ◽

pp. 324-324 ◽

Cited By ~ 6

Author(s):

Wolfram Koepf

Keyword(s):

Symmetric Functions ◽

Bounded Boundary Rotation ◽

Boundary Rotation

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On subclasses of close-to-convex functions of higher order

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s016117129200036x ◽

1992 ◽

Vol 15 (2) ◽

pp. 279-289 ◽

Cited By ~ 32

Author(s):

Khalida Inayat Noor

Keyword(s):

Convex Functions ◽

Analytic Functions ◽

Higher Order ◽

Arc Length ◽

Covering Theorem ◽

Bounded Boundary Rotation ◽

Boundary Rotation

The classesTk(ρ),0≤ρ<1,k≥2, of analytic functions, using the classVk(ρ)of functions of bounded boundary rotation, are defined and it is shown that the functions in these classes are close-to-convex of higher order. Covering theorem, arc-length result and some radii problems are solved. We also discuss some properties of the classVk(ρ)including distortion and coefficient results.

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