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On the order of strongly starlikeness in some classes of starlike functions

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Abstract

We consider the order of strongly starlikeness in the class of analytic functions f, f(0) =  0, f' (0) = 1, such that

$$\left|\frac{1 + zf^{\prime\prime}(z)/f^{\prime}(z)}{zf^{\prime}(z)/f(z)} - 1\right| < b \quad {\rm for} \quad z \in \mathbb{D}$$

. We consider also the same problem for α-convex functions of order β.

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References

  1. Brannan D. A., Kirwan W. E.: On some classes of bounded univalent functions. J. London Math. Soc. 1, 431–443 (1969)

    Article  MATH  MathSciNet  Google Scholar 

  2. Nunokawa M.: On properties of non-Carathéodory functions. Proc. Japan Acad., Ser. A 68, 152–153 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  3. Nunokawa M.: On the order of strongly starlikeness of strongly convex functions. Proc. Japan Acad., Ser. A 69, 234–237 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  4. P. T. Mocanu, Une propriété de convexité généralisée dans la théorie de la représentation conforme, Mathematica (Cluj), 11(34) (1969), 127–133.

  5. Obradović M., Tuneski N.: On the starlike criteria defined by Silverman. Fol. Scient. Univ. Tech. Res. 181, 59–64 (2000)

    Google Scholar 

  6. Silverman H.: Convex and starlike criteria. Int. Math. Math. Sci. 22, 75–79 (1999)

    Article  MATH  Google Scholar 

  7. J. Stankiewicz, Quelques problèmes extrèmaux dans les classes des fonctions α- angulairement ètoilèes, Ann. Univ. Mariae Curie-Skłodowska, Sect. A, 20 (1966), 59–75.

  8. N. Tuneski, On the quotient of the representations of convexity and starlikeness, Math. Nachr., 248/249 (2003), 200–203.

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Authors and Affiliations

  1. University of Gunma, Hoshikuki-cho 798-8, Chuou-Ward, Chiba, 260-0808, Japan

    M. Nunokawa

  2. Department of Mathematics, Rzeszów University of Technology, Al. Powstańców Warszawy 12, 35-959, Rzeszów, Poland

    J. Sokół

  3. Department of Mathematics, Lublin University of Technology, ul. Nadbystrzycka 38D, 20-618, Lublin, Poland

    K. Tra̧bka-wiȩcław

Authors
  1. M. Nunokawa
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  2. J. Sokół
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  3. K. Tra̧bka-wiȩcław
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Correspondence to J. Sokół.

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Nunokawa, M., Sokół, J. & Tra̧bka-wiȩcław, K. On the order of strongly starlikeness in some classes of starlike functions. Acta Math. Hungar. 145, 142–149 (2015). https://doi.org/10.1007/s10474-014-0467-4

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  • DOI: https://doi.org/10.1007/s10474-014-0467-4

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