Search

Your search keyword '"Masih, Vali Soltani"' showing total 10 results
Start Over Author "Masih, Vali Soltani"
10 results on '"Masih, Vali Soltani"'

3. Solution of the logarithmic coefficients conjecture in some families of univalent functions

Author

Kanas, Stanislawa and Masih, Vali Soltani

Subjects
Mathematics - Complex Variables
Abstract

For univalent and normalized functions $f$ the logarithmic coefficients $\gamma_n(f)$ are determined by the formula $\log(f(z)/z)=\sum_{n=1}^{\infty}2\gamma_n(f)z^n$. In the paper \cite{Pon} the authors posed the conjecture that a locally univalent function in the unit disk, satisfying the condition \[ \Re\left\{1+zf''(z)/f'(z)\right\}<1+\lambda/2\quad (z\in \mathbb{D}), \] fulfill also the following inequality: $$|\gamma_n(f)|\le \lambda/(2n(n+1)).$$ Here $\lambda$ is a real number such that $0<\lambda\le 1$. In the paper we confirm that the conjecture is true, and sharp., Comment: 7 figures added

Published
2020

6. On strongly starlike functions related to the Bernoulli lemniscate.

Author

Masih, Vali Soltani, Ebadian, Ali, and Sokół, Janusz

Subjects
STAR-like functions, CONVEX domains, UNIVALENT functions, LOGARITHMIC functions, HANKEL functions
Abstract

LetS*L(λ) be the class of functionsf, analytic in the unit disc Δ ={z:|z|<1}, with the normalization f(0) =f'(0)-1 = 0, which satisfy the conditionz f'(z)/f(z)≺(1 +z)λ, where≺is the subordination relation. The classS*L(λ) is a subfamily of the known class of strongly starlike functions of order λ. In this paper, the relations between S*L(λ) and other classes geometrically defined are considered. Also, we obtain some characteristics such as, bounds for coefficients, radius of convexity, the Fekete-Szeg ?o inequality, logarithmic coefficients and the second Hankel determinant inequality for functions belonging to this class. The univalent functionsfwhich satisfy the condition <{1 +zf"(z)/f'(z)} < 1 +λ/2, (z∈Δ) are also considered here. [ABSTRACT FROM AUTHOR]

Published
2022
Full Text
View/download PDF

Catalog

Books, media, physical & digital resources
See catalog results