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Starlikeness and Schwarzian derivatives of higher order of analytic functions

심영재|권오상
대한수학회 (The Korean Mathematical Society)|2017.01|대한수학회논문집 (Communications of the KMS)|제32권 제1호|pp. 93-106

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참고문헌

키워드

analytic functionsstarlike functionsdifferential subordinationadmissible functionsSchwarzian derivatives
주제분류수학

초록

In this paper we apply the third-order differential subordination results to normalized analytic functions in the open unit disk. We obtain appropriate classes of admissible functions and find some sufficient conditions of functions to be starlike associated with Tamanoi's Schwarzian derivative of third order. Several interesting examples are also discussed.

Abstract

In this paper we apply the third-order differential subordination results to normalized analytic functions in the open unit disk. We obtain appropriate classes of admissible functions and find some sufficient conditions of functions to be starlike associated with Tamanoi's Schwarzian derivative of third order. Several interesting examples are also discussed.

참고문헌 (13)

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  2. R. M. Ali, "Subordination and superordination on Schwarzian derivatives", J. Inequal. Appl, 2008, pp.18~ (2008)
  3. A. A. Antonino, "Third-order differential inequalities and subordinations in the complex plane", Complex Var. Elliptic Equ, 56(5), pp.439~454 (2011)
  4. R. Harmelin, "Aharonov invariants and univalent functions", Israel J. Math, 43(3), pp.244~254 (1982)
  5. M. P. Jeyaraman, "Third-order differential subordination of analytic functions", Acta Univ. Apulensis Math. Inform, 35, pp.187~202 (2013)
  6. S. A. Kim, "Invariant Schwarzian derivatives of higher order", Complex Anal. Oper. Theory, 5(3), pp.659~670 (2011)
  7. S. S. Miller, "Second order differential inequalities in the complex plane", J. Math. Anal. Appl, 65(2), pp.289~305 (1978)
  8. S. S. Miller, "Differential Subordinations: Theory and Applications" (2000), Marcel Dekker
  9. Z. Nehari, "The Schwarzian derivative and schlicht functions", Bull. Amer. Math. Soc, 55, pp.545~551 (1949)
  10. Z. Nehari, "Some criteria of univalence", Proc. Amer. Math. Soc, 5, pp.700~704 (1954)
  11. S. Owa, "An application of differential subordinations and some cri-teria for univalency", Bull. Aust. Math. Soc, 41(3), pp.487~494 (1990)
  12. E. Schippers, "Distortion theorems for higher order Schwarzian derivatives of univalent functions", Proc. Amer. Math. Soc, 128(11), pp.3241~3249 (2000)
  13. H. Tamanoi, "Higher Schwarzian operators and combinatorics of the Schwarzian deriv-ative", Math. Ann, 305(1), pp.127~151 (1996)

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