### $\lambda $-fractional properties of generalized Janowski functions in the unit disc.

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MSC 2010: 30C55, 30C45 Distortion and growth theorems are obtained.

Let Pn denote the class of analytic functions p(z) of the form p(z) = 1+cnzn + cn+1zn+1 + ... in the open unit disc U . Applying the result by S. S. Miller and P. T. Mocanu (J. Math. Anal. Appl. 65 (1978), 289-305), some interesting properties for p(z) concerned with Carath´eodory functions are discussed. Further, some corollaries of the results concerned with the result due to M. Obradović and S. Owa (Math. Nachr. 140 (1989), 97-102) are shown.

Let ${\mathcal{P}}_{n}$ denote the class of analytic functions $p\left(z\right)$ of the form $p\left(z\right)=1+{c}_{n}{z}^{n}+{c}_{n+1}{z}^{n+1}+\cdots $ in the open unit disc $\mathbb{U}$. Applying the result by S. S. Miller and P. T. Mocanu (J. Math. Anal. Appl. 65 (1978), 289-305), some interesting properties for $p\left(z\right)$ concerned with Caratheodory functions are discussed. Further, some corollaries of the results concerned with the result due to M. Obradovic and S. Owa (Math. Nachr. 140 (1989), 97-102) are shown.

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