Generalized Alpha-Close-to-Convex Functions

We define the classesGβ(α,k,γ)as follows:f∈Gβ(α,k,γ)if and only if, forz∈E={z∈ℂ:|z|<1},|arg{(1-α2z2)f′(z)/e−iβϕ′(z)}|≤γπ/2,0<γ≤1;α∈[0,1];β∈(−π/2,π/2), whereϕis a function of bounded boundary rotation. Coefficient estimates, an inclusion result, arclength problem, and some other properties of these classes are studied.

Close-to-convex functions and functions of bounded boundary rotation

Complex Variables Theory and Application An International Journal ◽

10.1080/17476938408814073 ◽

1984 ◽

Vol 3 (1-3) ◽

pp. 205-210

Author(s):

Albert Pfluger

Keyword(s):

Convex Functions ◽

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 ◽

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.

Multivalent Functions of Bounded Boundary Rotation and Weakly Close-to-Convex Functions

Proceedings of the London Mathematical Society ◽

10.1112/plms/s3-51.3.478 ◽

1985 ◽

Vol s3-51 (3) ◽

pp. 478-500 ◽

Cited By ~ 6

Author(s):

Abdallah Lyzzaik

Keyword(s):

Convex Functions ◽

On Convex Functions with Complex Order Through Bounded Boundary Rotation

Mathematics in Computer Science ◽

10.1007/s11786-019-00405-8 ◽

2019 ◽

Vol 13 (3) ◽

pp. 433-439

Author(s):

S. Melike Aydoğan ◽

F. Müge Sakar

Keyword(s):

Convex Functions ◽

Complex Order ◽

On functions of bounded boundary rotation I

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s001309150001302x ◽

1969 ◽

Vol 16 (4) ◽

pp. 339-347 ◽

Cited By ~ 14

Author(s):

D. A. Brannan

Keyword(s):

Upper Bound ◽

Convex Functions ◽

Image Domain ◽

Basic Properties ◽

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.

On strongly starlike and strongly convex functions with bounded radius and bounded boundary rotation

Journal of Inequalities and Applications ◽

10.1186/s13660-020-02391-z ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Sabir Hussain ◽

Khalil Ahmad

Keyword(s):

Convex Functions ◽

Strongly Convex Functions ◽

Strongly Convex ◽

Boundary Rotation ◽

Strongly Starlike

Toeplitz matrices whose elements are coefficients of Bazilevič functions

Open Mathematics ◽

10.1515/math-2018-0093 ◽

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 ◽

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.