Results 1 to 10 of about 47,345 (292)
On Starlike and Close-to-Convex Functions [PDF]
Proceedings of the London Mathematical Society, 1963 Peer Reviewed ; http://deepblue.lib.umich.edu/bitstream/2027.42/135466/1/plms0290 ...
Pommerenke, Christian
core +5 more sources
Bounded Doubly Close-to-Convex Functions [PDF]
Abstract and Applied Analysis, 2014 We consider a new classCC(α,β)of bounded doubly close-to-convex functions. Coefficient bounds, distortion theorems, and radius of convexity for the classCC(α,β)are investigated. A corresponding class of doubly close-to-starlike functionsS*S(α,β)is also considered.
Dorina Răducanu
core +6 more sources
Generalized Alpha‐Close‐to‐Convex Functions [PDF]
International Journal of Mathematics and Mathematical Sciences, 2009 We define the classes Gβ(α, k, γ) as follows: f ∈ Gβ(α, k, γ) if and only if, for z ∈ 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), where ϕ is a function of bounded boundary rotation.
Halit Orhan +2 more
core +7 more sources
COEFFICIENT CONDITIONS FOR HARMONIC CLOSE-TO-CONVEX FUNCTIONS [PDF]
Abstract and Applied Analysis, 2012 New sufficient conditions, concerned with the coefficients of harmonic functions $f(z)=h(z)+\bar{g(z)}$ in the open unit disk $\mathbb{U}$ normalized by $f(0)=h(0)=h'(0)-1=0$, for $f(z)$ to be harmonic close-to-convex functions are discussed. Furthermore,
HAYAMI, TOSHIO
core +8 more sources
On the definition of a close‐to‐convex function [PDF]
International Journal of Mathematics and Mathematical Sciences, 1978 The standard definition of a close‐to‐convex function involves a complex numerical factor eiβ which is on occasion erroneously replaced by 1. While it is known to experts in the field that this replacement cannot be made without essentially changing the class, explicit reasons for this fact seem to be lacking in the literature.
Goodman, A. W., Saff, E. B.
openaire +3 more sources
On a Subclass of Close-to-Convex Functions [PDF]
Bulletin of the Iranian Mathematical Society, 2018 11 ...
Yao Liang Chung +2 more
openaire +3 more sources
SOME CONDITIONS ON STARLIKE AND CLOSE TO CONVEX FUNCTIONS [PDF]
, 2022 Many mathematical concepts are explained when viewed through complex function theory. We are here basically concerned with the form f(z) = a(0) + a(1)z + a(2)z(2) +....
Mert, Oya +2 more
core +1 more source
On a subclass of close-to-convex functions
Applied Mathematics Letters, 2010 AbstractWe consider a subclass of the class of close-to-convex functions. We show the relationship between our class and the appropriate subordination. Moreover, we give the coefficient estimates and a sufficient condition for functions to belong to the class investigated. Finally, we obtain the distortion and the growth theorems. The results presented
Joanna Kowalczyk, Edyta Leś-Bomba
openaire +4 more sources
On a generalization of close‐to‐convexity [PDF]
International Journal of Mathematics and Mathematical Sciences, 1982 A class Tk of analytic functions in the unit disc is defined in which the concept of close‐to‐convexity is generalized. A necessary condition for a function f to belong to Tk, raduis of convexity problem and a coefficient result are solved in this paper.
openaire +3 more sources
On a subclass of close-to-convex harmonic mappings [PDF]
Journal of Classical Analysis, 2020 For $ > -1$ and $ >0, $ let $\mathcal{B}_{\mathcal{H}}^0( , )$ denote the class of sense preserving harmonic mappings $f=h+\overline{g}$ in the open unit disk $\mathbb{D}$ satisfying $|zh''(z)+ (h'(z)-1)|\leq -|zg''(z)+ g'(z)|.$ First, we establish that each function belonging to this class is close-to-convex in the open unit disk if $ \
Mathi, Manivannan +1 more
openaire +2 more sources