Certain Properties of a Generalized Class of Analytic Functions Involving Some Convolution Operator

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
F.S.A. Malik, Nusrat Ahmed Dar, Chitaranjan Sharma
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引用次数: 1

Abstract

We use the concept of convolution to introduce and study the properties of a unified family $\mathcal{TUM}_\gamma(g,b,k,\alpha)$, $(0\leq\gamma\leq1,\,k\geq0)$, consisting of uniformly $k$-starlike and $k$-convex functions of complex order $b\in\mathbb{C}\setminus\{0\}$ and type $\alpha\in[0,1)$. The family $\mathcal{TUM}_\gamma(g,b,k,\alpha)$ is a generalization of several other families of analytic functions available in literature. Apart from discussing the coefficient bounds, sharp radii estimates, extreme points and the subordination theorem for this family, we settle down the Silverman's conjecture for integral means inequality. Moreover, invariance of this family under certain well-known integral operators is also established in this paper. Some previously known results are obtained as special cases.
一类包含卷积算子的广义解析函数的某些性质
我们使用卷积的概念来引入和研究统一族$\mathcal的性质{TUM}_\gamma(g,b,k,\alpha)$,$(0\leq\gamma\leq1,\,k\geq0)$,由$k$-星形和$k$-复阶凸函数$b\in\mathbb{C}\setminus\{0\}$和类型$\alpha\in[0,1)$组成{TUM}_\gamma(g,b,k,\alpha)$是文献中其他几个分析函数族的推广。除了讨论该族的系数界、锐半径估计、极值点和隶属定理外,我们还建立了积分均值不等式的Silverman猜想。此外,本文还建立了该族在某些已知积分算子下的不变性。一些先前已知的结果是作为特例获得的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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