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We consider a sufficient condition for $w(z)$, analytic in $|z|<1$, to be bounded in $|z|<1$, where $w(0)=w'(0)=0$. We apply it to the meromorphic starlike functions. Also, a certain Briot-Bouquet differential subordination is considered. Moreover, we prove that if $p(z)+zp'(z)\phi(p(z))\prec h(z)$, then $p(z)\prec h(z)$, where $h(z)=[(1+z)(1-z)]^{\alpha}$, under some additional assumptions on $\phi(z)$.
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참고문헌 (10)
참고문헌 신청
H. Al-Amiri / 1995 / Some simple criteria of starlikeness and convexity for meromorphic functions / Mathematica 37(60)(1-2):11~21
S. Fukui / 1980 / An extension of a theorem of S. Ruscheweyh / Bull. Fac. Ed. Wakayama Univ. Natur. Sci 29:1~3
I. S. Jack / 1971 / Functions starlike and convex of order α / J. London Math. Soc 3:469~474
D. I. Hallenbeck / 1975 / Subordination by convex functions / Proc. Amer. Math. Soc 52:191~195
S. S. Miller / 2000 / Differential Subordinations: Theory and Applications / Marcel Dekker Inc.
S. Fukui / 1980 / An extension of a theorem of S. Ruscheweyh / Bull. Fac. Ed. Wakayama Univ. Natur. Sci 29:1~3
I. S. Jack / 1971 / Functions starlike and convex of order α / J. London Math. Soc 3:469~474
D. I. Hallenbeck / 1975 / Subordination by convex functions / Proc. Amer. Math. Soc 52:191~195
S. S. Miller / 2000 / Differential Subordinations: Theory and Applications / Marcel Dekker Inc.
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