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Języki publikacji
Abstrakty
Let $𝓑₀^{(R)}(b)$ denote the class of functions F(z) = b + A₁z + A₂z² + ...$ analytic and univalent in the unit disk U which satisfy the conditions: F(U) ⊂ U, 0 ∉ F(U), $Im F^{(n)}(0) = 0$. Using Loewner's parametric method we obtain lower and upper bounds of A₂ in $𝓑₀^{(R)}(b)$ and functions for which these bounds are realized. The class $𝓑₀^{(R)}(b)$, introduced in [6], is a subclass of the class $𝓑_u$ of bounded, non-vanishing univalent functions in the unit disk. This last class and closely related ones have been studied by various authors in [1]-[4]. We mention in particular the paper of D. V. Prokhorov and J. Szynal [5], where a sharp upper bound for the second coefficient in $𝓑_u$ is given.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
119-123
Opis fizyczny
Daty
wydano
1998
otrzymano
1996-11-05
poprawiono
1997-02-15
Twórcy
autor
- Institute of Mathematics, Silesian Technical University, Ul. Kaszubska 23, 44-100 Gliwice, Poland
Bibliografia
- [1] P. Duren and G. Schober, Nonvanishing univalent functions, Math. Z. 170 (1980), 195-216.
- [2] C. Horowitz, Coefficients of nonvanishing functions in $H^∞$, Israel J. Math. 30 (1978), 285-291.
- [3] J. Hummel, S. Scheinberg and L. Zalcman, A coefficient problem for bounded nonvanishing functions, J. Anal. Math. 31 (1977), 169-190.
- [4] J. Krzyż, Coefficient problem for bounded nonvanishing functions, Ann. Polon. Math. 70 (1968), 314.
- [5] D. V. Prokhorov and J. Szynal, Coefficient estimates for bounded nonvanishing functions, Bull. Acad. Polon. Sci. Sér. Sci. Math. 29 (1981), 223-230.
- [6] J. Śladkowska, On univalent, bounded, non-vanishing and symmetric functions in the unit disk, Ann. Polon. Math. 64 (1996), 291-299.
- [7] O. Tammi, Extremum Problems for Bounded Univalent Functions, Lecture Notes in Math. 646, Springer, 1978.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv68z2p119bwm