Notes on certain analytic functions

Authors : Emel Yavuz DUMAN, Shigeyoshi OWA

Pages : 279-283

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :Let $\mathcal{A}insert ignore into journalissuearticles values(n);$ be the class of functions $$finsert ignore into journalissuearticles values(z);=a_nz^n + a_{n+1}z^{n+1}+\cdots insert ignore into journalissuearticles values(n\in \mathbb{N});,$$ which are analytic in the open unit disk $\mathbb{U}$, where $a_n \neq 0$. For $finsert ignore into journalissuearticles values(z);\in \mathcal{A}insert ignore into journalissuearticles values(n);$, Miller and Mocanu in 1978 showed a very interesting result for $finsert ignore into journalissuearticles values(z);$. Applying the result due to Miller and Mocanu, we would like to consider some new results for such functions. Our results in this paper are generalizations for results by Nunokawa in 1992.
Keywords : Analytic function, the class mathcal S n, alpha, , the class mathcal K n, alpha,