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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.10 No.4

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ON THE FEKETE-SZEG？O PROBLEMFOR CERTAIN ANALYTIC FUNCTIONS

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2003, v.10 no.4, pp.265-271
Kwon, Oh-Sang
Cho, Nak-Eun
Kwon,, O. , & Cho,, N. (2003). ON THE FEKETE-SZEG？O PROBLEMFOR CERTAIN ANALYTIC FUNCTIONS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 10(4), 265-271.

Abstract

Let <TEX>$CS_\alpha(\beta)$</TEX> denote the class of normalized strongly <TEX>$\alpha$</TEX>-close-to-convex functions of order <TEX>$\beta$</TEX>, defined in the open unit disk <TEX>$\cal{U}$</TEX> of <TEX>$\mathbb{C}$</TEX. by , <TEX>${\mid}arg{(1-{\alpha})\frac{f(z)}{g(z)}+{\alpha}\frac{zf'(z)}{g(z)}}{\mid}\;\leq\frac{\pi}{2}{\beta}(\alpha,\beta\geq0)$</TEX> such that <TEX>$g\; \in\;S^{\ask}$</TEX>, the class of normalized starlike unctions. In this paper, we obtain the sharp Fekete-Szego inequalities for functions belonging to <TEX>$CS_\alpha(\beta)$</TEX>.

keywords
univalent, starlike, Fekete-Szego problem, close-to-star, close-to-convex, strongly <tex> $\alpha$</tex>-close-to-convex

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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