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Differential Subordination Properties of Sokol-Stankiewicz Starlike Functions

Rashidah Omar|Suzeini Abdul Halim
경북대학교 자연과학대학 수학과|2013.09|Kyungpook Mathematical Journal|제53권 제3호|pp. 459-465

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참고문헌

키워드

Analytic functionsdifferential subordinationSok´o l-Stankiewicz starlike functions.
주제분류수학

초록

Let p(z) be an analytic function defined on the open unit disk D and p(0) = 1. Condition β in terms of complex numbers D and real E with −1 < E < 1 and |D| ≤ 1is determined such that 1 + βzp0(z) ＜ 1+Dz/1+Ez implies p(z) ＜1 + z. Furthermore, theexpression 1 + βzp'(z)/p(z) and 1 + βzp'(z)/p2(z) are considered in obtaining similar results.

Abstract

Let p(z) be an analytic function defined on the open unit disk D and p(0) = 1. Condition β in terms of complex numbers D and real E with −1 < E < 1 and |D| ≤ 1is determined such that 1 + βzp0(z) ＜ 1+Dz/1+Ez implies p(z) ＜1 + z. Furthermore, theexpression 1 + βzp'(z)/p(z) and 1 + βzp'(z)/p2(z) are considered in obtaining similar results.

참고문헌 (10)

  1. W. Janowski, "Some extremal problems for certain families of analytic functions I", Ann. Polon. Math., 28, pp.297~326 (1973)
  2. S. S. Miller, "Differential subordination, theory and application" (2000), Marcel Dekker, Inc.
  3. M. Nunokawa, "One criterion for univalency", Proc. Amer. Math. Soc., 106(4), pp.1035~1037 (1989)
  4. R. M. Ali, "First order differential subordination for functions associated with the lemniscate of Bernoulli", Taiwanese J. Math, 16(3), pp.1017~1026 (2012)
  5. R. M. Ali, "Sufficient conditions for Janowski starlikeness, International J. Math. and Mathematical Sciences", International J. Math. and Mathematical Sciences, pp.7~ (2007)
  6. J. Sok´o l, "Radius of convexity of some subclasses of strongly starlike functions", Folia Scient. Univ. Tech. Resoviensis, Mat., 19, pp.101~105 (1996)
  7. J. Sok´o l, "Radius problems in the class SL?", Applied Mathematics and Computation, 214, pp.569~573 (2009)
  8. Janusz Sokol, "Coffcient Estimates in a Class of Strongly Starlike Functions", Kyungpook Mathematical Journal, 49(2), pp.349~353 (2009), 경북대학교 자연과학대학 수학과
  9. J. Sok´o l, "On application of certain sufficient condition for starlikeness", J. Math. and Appl., 30, pp.131~135 (2008)
  10. J. Sok´o l, "On sufficient condition to be in a certain subclass of starlike functions defined by subordination", Applied Mathematics and Computation, 190, pp.237~241 (2007)

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