An Application of Jackson's $(p, q)$-Derivative to a Subclass of Starlike Functions with Negative Coefficients

Feras Yousef; Amal Al-Shible; Sibel Yalçın

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arXiv · 1903.01336

An Application of Jackson's $(p, q)$-Derivative to a Subclass of Starlike Functions with Negative Coefficients

Feras Yousef·Amal Al-Shible·Sibel Yalçın

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Abstract

In this paper, we introduce and investigate the subclass $\mathcal{P}_{p,q}^{\xi ,\kappa}(\tau, \eta)$ of starlike functions with negative coefficients by using the differential operator $\Upsilon_{\tau ,p,q}^{\xi ,\kappa}$. Coefficient inequalities, growth and distortion theorems, closure theorems, and some properties of several functions belonging to this class are obtained. We also determine the radii of close-to-convexity, starlikeness, and convexity for functions belonging to the class $\mathcal{P}_{p,q}^{\xi ,\kappa}(\tau, \eta)$. Furthermore, we obtain the integral means inequality and neighborhood results for functions belonging to the class $\mathcal{P}_{p,q}^{\xi ,\kappa}(\tau, \eta)$. The results presented in this paper generalize or improve those in related works of several earlier authors.

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Feras Yousef, Amal Al-Shible, Sibel Yalçın. 2019-03-04. An Application of Jackson's $(p, q)$-Derivative to a Subclass of Starlike Functions with Negative Coefficients. https://arxiv.org/abs/1903.01336

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