호남수학학술지 (Honam Mathematical Journal)

  • 제23권1호
  • /
  • Pages.41-50
  • /
  • 2001
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  • 1225-293X(pISSN)
  • /
  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
권호 표지

SUBORDINATION ON δ-CONVEX FUNCTIONS IN A SECTOR

  • MARJONO, MARJONO (Dept. of Mathematics, University of Brawijaya) ;
  • THOMAS, D.K. (Dept. of Mathematics, University of Wales)
  • 투고 : 2001.03.02
  • 발행 : 2001.07.30
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초록

This paper concerns with the subclass of normalized analytic function f in D = {z : |z| < 1}, namely a ${\delta}$-convex function in a sector. This subclass is denoted by ${\Delta}({\delta})$, where ${\delta}$ is a real positive. Given $0<{\beta}{\leq}1$ then for $z{\in}D$, the exact ${\alpha}({\beta},\;{\delta})$ is found such that $f{\in}{\Delta}({\delta})$ implies $f{\in}S^*({\beta})$, where $S^*({\beta})$ is starlike of order ${\beta}$ in a sector. This work is a more general version of the result of Nunokawa and Thomas [11].

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참고문헌

  1. Univalent Functions Duren, P.L.
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  3. Univalent Functions Goodman, A.W.
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  5. J. London Math. Soc. v.23 no.2 A Subordination for convex functions of order ${\alpha}$ MacGregor, T.H.
  6. Proceeding of the ISSM An Other Version of the Miller-Mocanu Lemma Marjono
  7. Math. Japonica v.51 no.3 A Sufficient Condition for Starlikeness for Analytic Functions Marjono
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  10. Math. Ann. v.107 Untersuchungen uber Schlichte Abbildung Marx, A.
  11. J. Austral. Math. Soc. Ser. v.A 60 no.3 On convex and starlike functions in a sector Nunokawa, M.;Thomas, D.K.
  12. On ${\alpha}$-convexity and starlikeness Obradovic, M.;Fukui, S.;Sekine, T.
  13. Math. Z. v.37 Beitrage zur Theorie der Schlichten Funktionen Strohhacker, E.
  14. J. London Math. Soc. v.21 no.2 A remark on convex and starlike functions Wilken, D.R.;Feng, J.