Strongly gamma-starlike functions of order alpha

Mamoru Nunokawa, Janusz Sokół

Abstract


In this work we consider the class of analytic functions \(\mathcal{G}(\alpha,\gamma)\), which is a subset of gamma-starlike functions introduced by Lewandowski, Miller and Złotkiewicz in Gamma starlike functions, Ann. Univ. Mariae Curie-Skłodowska, Sect. A 28 (1974), 53–58. We discuss the order of strongly starlikeness and the order of strongly convexity in this subclass.

Keywords


Strongly starlike functions of order alpha; convex functions of order alpha; strongly starlike functions of order alpha; gamma-starlike functions; Nunokawa's Lemma.

Full Text:

PDF

References


Brannan, D. A., Kirwan, W. E., On some classes of bounded univalent functions, J. London Math. Soc. 1 (2) (1969), 431–443.

Lewandowski, Z., Sur l’identite de certaines classes de fonctions univalentes, II, Ann. Univ. Mariae Curie-Skłodowska Sect. A 14 (1960), 19–46.

Lewandowski, Z., Miller, S., Złotkiewicz, E., Gamma starlike functions, Ann. Univ. Mariae Curie-Skłodowska Sect. A 28 (1974), 53–58.

Nunokawa, M., On properties of non-Caratheodory functions, Proc. Japan Acad. Ser. A 68 (6) (1992), 152–153.

Nunokawa, M., On the order of strongly starlikeness of strongly convex functions, Proc. Japan Acad. Ser. A 69 (7) (1993), 234–237.

Robertson, M. S., On the theory of univalent functions, Ann. Math. 37 (1936), 374–408.

Sokół, J., On sufficient condition to be in a certain subclass of starlike functions defined by subordination, Appl. Math. Comp. 190 (2007), 237–241.

Stankiewicz, J., Quelques problemes extr emaux dans les classes des fonctions - angulairement etoilees, Ann. Univ. Mariae Curie-Skłodowska Sect. A 20 (1966), 59–75.

Wilken, D. R., Feng, J, A remark on convex and starlike functions, J. London Math. Soc. 21 (2) (1980), 287–290.




DOI: http://dx.doi.org/10.17951/a.2013.67.2.43-51
Data publikacji: 2015-07-15 00:00:00
Data złożenia artykułu: 2016-01-12 09:59:21

Refbacks

  • There are currently no refbacks.


Copyright (c) 2016 Mamoru Nunokawa, Janusz Sokół