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In this paper, a generalized boundary version of Carath\'{e}od\-ory's inequality for holomorphic function satisfying $f(z)=f(0)+a_{p}z^{p}+\cdots,$ and $\Re f(z)\leq A$ for $\left\vert z\right\vert <1$ is investigated. Also, we obtain sharp lower bounds on the angular derivative $f^{\prime }(c)$ at the point $c$ with $\Re f(c)=A$. The sharpness of these estimates is also proved.
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참고문헌 (19)
참고문헌 신청
Tuğba AKYEL / 2015 / A SHARP SCHWARZ LEMMA AT THE BOUNDARY / 순수 및 응용수학 22(3):263~273
T. Aliyev Azeroglu / 2013 / A refined Schwarz inequality on the boundary / Complex Var. Elliptic Equ 58(4):571~577
H. P. Boas / 2010 / Julius and Julia: Mastering the art of the Schwarz lemma / Amer. Math. Monthly 117(9):770~785
D. M. Burns / 1994 / Rigidity of holomorphic mappings and a new Schwarz lemma at the boundary / J. Amer. Math. Soc 7(3):661~676
D. Chelst / 2001 / A generalized Schwarz lemma at the boundary / Proc. Amer. Math. Soc 129(11):3275~3278
T. Aliyev Azeroglu / 2013 / A refined Schwarz inequality on the boundary / Complex Var. Elliptic Equ 58(4):571~577
H. P. Boas / 2010 / Julius and Julia: Mastering the art of the Schwarz lemma / Amer. Math. Monthly 117(9):770~785
D. M. Burns / 1994 / Rigidity of holomorphic mappings and a new Schwarz lemma at the boundary / J. Amer. Math. Soc 7(3):661~676
D. Chelst / 2001 / A generalized Schwarz lemma at the boundary / Proc. Amer. Math. Soc 129(11):3275~3278
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