Taiwanese Journal of Mathematics

COEFFICIENT ESTIMATES FOR CERTAIN SUBCLASSES OF ANALYTIC FUNCTIONS OF COMPLEX ORDER

Qing-Hua Xu, Ying-Chun Gui, and H. M. Srivastava

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Abstract

In this paper, we introduce and investigate each of the following subclasses:  $$\mathcal{S}_g(\lambda, \gamma)\,\,\,\, \text{and} \,\,\,\, \mathcal{K}_g(\lambda, \gamma, m; u) \,\,\,\, \Big(0\!\leqq\! \lambda\! \leqq\! 1; u\!\in\! \mathbb{R}\setminus (-\infty, -1]; \ m\in \mathbb{N}\setminus\{1\}\Big) $$ of analytic functions of complex order $\gamma \in \mathbb{C} \setminus \{0\}$, $g: \mathbb{U} \rightarrow \mathbb{C}$ being some suitably constrained convex function in the open unit disk $\mathbb{U}$. We obtain coefficient bounds and coefficient estimates involving the Taylor-Maclaurin coefficients of the function $f(z)$ when $f(z)$ is in the class $\mathcal{S}_g(\lambda,\gamma)$ or in the class $\mathcal{K}_g(\lambda,\gamma,m;u)$. The various results, which are presented in this paper, would generalize and improve those in related works of several earlier authors.

Article information

Source
Taiwanese J. Math., Volume 15, Number 5 (2011), 2377-2386.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406441

Digital Object Identifier
doi:10.11650/twjm/1500406441

Mathematical Reviews number (MathSciNet)
MR2880411

Zentralblatt MATH identifier
1238.30015

Subjects
Primary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
Secondary: 34-99

Keywords
coefficient bounds analytic functions of complex order starlike and convex functions of complex order Cauchy-Euler differential equations non-homogenous differential equations principle of subordination between analytic function

Citation

Xu, Qing-Hua; Gui, Ying-Chun; Srivastava, H. M. COEFFICIENT ESTIMATES FOR CERTAIN SUBCLASSES OF ANALYTIC FUNCTIONS OF COMPLEX ORDER. Taiwanese J. Math. 15 (2011), no. 5, 2377--2386. doi:10.11650/twjm/1500406441. https://projecteuclid.org/euclid.twjm/1500406441


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