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Search Results: 1 - 10 of 2821 matches for " Univalent functions "
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A Certain Subclass of Analytic Functions  [PDF]
Young Jae Sim, Oh Sang Kwon
Advances in Pure Mathematics (APM) , 2012, DOI: 10.4236/apm.2012.24038
Abstract: In the present paper, we introduce a class of analytic functions in the open unit disc by using the analytic function qα(z)=3/(3+(α-3)z-αz2), which was investigated by Sokó? [1]. We find some properties including the growth theorem or the coefficient problem of this class and we find some relation with this new class and the class of convex functions.
On the coefficient domains of univalent functions
M. M. Elhosh
International Journal of Mathematics and Mathematical Sciences , 1990, DOI: 10.1155/s016117129000062x
Abstract: Coefficient domains for functions whose derivative has positive real part in the interior of an ellipse are given in this paper.
On the asymptotic Bieberbach conjecture
Mauriso Alves,Armando J. P. Cavalcante
International Journal of Mathematics and Mathematical Sciences , 1982, DOI: 10.1155/s0161171282000507
Abstract: The set S consists of complex functions f, univalent in the open unit disk, with f(0)=f ¢ € 2(0) ¢ ’1=0. We use the asymptotic behavior of the positive semidefinite FitzGerald matrix to show that there is an absolute constant N0 such that, for any f(z)=z+ ¢ ‘n=2 ¢ anzn ¢ S with |a3| ¢ ‰ ¤2.58, we have |an|N0.
Coefficient Estimates for a Certain General Subclass of Analytic and Bi-Univalent Functions  [PDF]
Nanjundan Magesh, Jagadeesan Yamini
Applied Mathematics (AM) , 2014, DOI: 10.4236/am.2014.57098

Motivated and stimulated especially by the work of Xu et al. [1], in this paper, we introduce and discuss an interesting subclass \"\" of analytic and bi-univalent functions defined in the open unit disc U. Further, we find estimates on the coefficients \"\" and \"\" for functions in this subclass. Many relevant connections with known or new results are pointed out.

On the definition of a close-to-convex function
A. W. Goodman,E. B. Saff
International Journal of Mathematics and Mathematical Sciences , 1978, DOI: 10.1155/s0161171278000150
Abstract: The standard definition of a close-to-convex function involves a complex numerical factor ei 2 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. Our purpose is to fill this gap, and in so doing we are lead to a new coefficient problem which is solved for n=2, but is open for n>2.
Integral operators and univalent functions
Kiah Wah Ong,Sin Leng Tan,Yong Eng Tu
Tamkang Journal of Mathematics , 2012, DOI: 10.5556/j.tkjm.43.2012.215-221
Abstract: In this paper, we define two new integral operators $L^k$ and $L_k$ which are iterative in nature. We show that for $f(z)=z+a_2z^2+ cdots +a_nz^n +cdots$ with radius of convergence larger than one, $L^kf(z)$ and $L_kf(z)$ when restricted on $E={z:|z|<1}$ will eventually be univalent for large enough $k$. We then show that these are the best possible results by demonstrating that there exists a holomorphic function $T(z)$ in normalized form and with radius of convergence equal to one such that $L^kT(z)$ and $L_kT(z)$ fail to be univalent when restricted to $E$ for every $kin mathbb{N}$.
Two criteria for univalency
N. Samaris
International Journal of Mathematics and Mathematical Sciences , 1996, DOI: 10.1155/s0161171296000579
Abstract: In the present paper we give two criteria for the functions f(z)=z+ ±2z2+ ¢ € | to be univalent in |z|<1.
On a class of univalent functions
Dinggong Yang,Jinlin Liu
International Journal of Mathematics and Mathematical Sciences , 1999, DOI: 10.1155/s0161171299226051
Abstract: We consider the class of univalent functions defined by the conditions f(z)/z ¢ ‰ 0 and |(z/f(z)) ¢ € 2 ¢ € ¢ € 2| ¢ ‰ ¤ ±,|z|<1, where f(z)=z+ ¢ ˉ is analytic in |z|<1 and 0< ± ¢ ‰ ¤2.
Remark on functions with all derivatives univalent
M. Lachance
International Journal of Mathematics and Mathematical Sciences , 1980, DOI: 10.1155/s0161171280000142
Abstract: An attractive conjecture is discounted for the class of normalized univalent functions whose derivatives are also univalent.
Typically real functions and typically real derivatives
S. Y. Trimble
International Journal of Mathematics and Mathematical Sciences , 1987, DOI: 10.1155/s0161171287000577
Abstract: Sufficient conditions, in terms of typically real derivatives, are given which force functions to be univalent.
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