Duality on a certain class of analytic functions related to parabolic domain

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Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Sciences, Urmia University. Urmia, Iran

Abstract

In the present paper a certain subclass of analytic functions related to parabolic domains is defined. We characterize duality of the class $ \small
        M(\alpha) = \left\{ f \in \mathcal{A} : \operatorname{Re} \{ \alpha\frac{f(z)}{z} + (1 - \alpha) f'(z) \} >\left|\alpha\frac{f(z)}{z} + (1 - \alpha) f'(z) -1\right|,\ z \in \mathbb{D} \right\},$ which gives some interesting results such as neighborhood, necessary and sufficient condition for normalized analytic function $f$ in open unit disk $\mathbb{D}$ to be in $M(\alpha)$ in terms of convolution.

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References

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Journal of Mahani Mathematical Research

Articles in Press, Accepted Manuscript
Available Online from 09 July 2026

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  • Receive Date: 10 May 2026
  • Revise Date: 15 June 2026
  • Accept Date: 02 July 2026

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