Emel YAVUZ, Shigeyoshi OWA

Notes on certain analytic functions

ISSN: 1300-0098
Yayın Aralığı: 6
Yayıncı: TÜBİTAK

Let A(n) be the class of functions $f(z)=a_nz^n+a_{n+1^{z^{n+1}}+...(ninmathbb{N})}$ which are analytic in the open unit disk U, where an ̸= 0. For f(z) 2 A(n) , Miller and Mocanu in 1978 showed a veryinteresting result for f(z) . Applying the result due to Miller and Mocanu, we would like to consider some new resultsfor such functions. Our results in this paper are generalizations for results by Nunokawa in 1992.

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[2] Miller SS, Mocanu PT. Second order differential inequalities in the complex plane. J Math Anal Appl 1978; 65: 289-305.
[3] Nunokawa M. On properties of non-Carathéodory functions. Proc Japan Acad 1992; 68: 152-153.