On a subclass of the generalized Janowski type functions of complex order

Year 2020, Volume: 49 Issue: 5, 1726 - 1734, 06.10.2020

Öznur Özkan Kılıç , Nuray Eroğlu

https://doi.org/10.15672/hujms.605621

Abstract

In this paper, we introduce the class $\mathcal {JR}^{\lambda}_{b}\left(\alpha,\beta, \delta, A,B\right)$ of generalized Janowski type functions of complex order defined by using the Ruscheweyh derivative operator in the open unit disc $ \mathbb D=\left \{z\in \mathbb C: \left \vert z\right \vert <1\right \}$. The bound for the n-th coefficient and subordination relation are obtained for the functions belonging to this class. Some consequences of our main theorems are same as the results obtained in the earlier studies.

Keywords

Analytic function, Subordination, $ \lambda$-spirallike function, $ \lambda$-Robertson function, $ \lambda$-close-to-spirallike function, $ \lambda$-close-to-Robertson function, Ruscheweyh derivative operator

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