논문KCI 등재
On the coefficients of gamma-starlike functions
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We give several sharp estimates for some initial coefficients problems for the so-called gamma starlike functions $f$, analytic and univalent in the unit disk $\mathbb{D}:=\{z\in\mathbb{C}:|z|<1\}$, and normalized so that $f(0)=0=f'(0)-1$, and satisfying $\real \Big[\Big(1+\frac{zf''(z)}{f'(z)}\Big)^{\gamma } \Big(\frac{zf'(z)}{f(z)}\Big)^{1-\gamma}\Big]>0$.
Abstract
We give several sharp estimates for some initial coefficients problems for the so-called gamma starlike functions $f$, analytic and univalent in the unit disk $\mathbb{D}:=\{z\in\mathbb{C}:|z|<1\}$, and normalized so that $f(0)=0=f'(0)-1$, and satisfying $\real \Big[\Big(1+\frac{zf''(z)}{f'(z)}\Big)^{\gamma } \Big(\frac{zf'(z)}{f(z)}\Big)^{1-\gamma}\Big]>0$.
참고문헌 (9)
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- A. Janteng, "Hankel determinant for starlike and convex functions", Int. J. Math. Anal. (Ruse), 1(13-16), pp.619~625 (2007)
- P. K. Kulshrestha, "Coeffcients for alpha-convex univalent functions", Bull. Amer. Math. Soc., 80, pp.341~342 (1974)[DOI]
- Z. Lewandowski, "Gamma-starlike functions", Ann. Univ. Mariae Curie-Sk lodowska Sect. A, 28, pp.53~58 (1974)
- R. J. Libera, "Early coeffcients of the inverse of a regular convex function", Proc. Amer. Math. Soc., 85(2), pp.225~230 (1982)[DOI]
- S. S. Miller, "All <TEX>${\alpha}$<", TEX>-convex functions are starlike, 1972, pp.17, 1395~1397
- S. S. Miller, "All <TEX>${\alpha}$<", TEX>-convex functions are univalent and starlike, 1973, pp.37, 553~554
- P. G. Todorov, "Explicit formulas for the coeffcients of <TEX>${\alpha}$<", TEX>-convex functions, <TEX>${\alpha}{\geq}0$<, Canad. J. Math., pp.1987, 39(4)[DOI]
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