F.S.A. Malik, Nusrat Ahmed Dar, Chitaranjan Sharma
{"title":"Certain Properties of a Generalized Class of Analytic Functions Involving Some Convolution Operator","authors":"F.S.A. Malik, Nusrat Ahmed Dar, Chitaranjan Sharma","doi":"10.34198/EJMS.7121.4976","DOIUrl":null,"url":null,"abstract":"We use the concept of convolution to introduce and study the properties of a unified family \n $\\mathcal{TUM}_\\gamma(g,b,k,\\alpha)$, \n $(0\\leq\\gamma\\leq1,\\,k\\geq0)$, \n consisting of uniformly $k$-starlike and $k$-convex functions of \n complex order $b\\in\\mathbb{C}\\setminus\\{0\\}$ \n and type $\\alpha\\in[0,1)$.\n The family $\\mathcal{TUM}_\\gamma(g,b,k,\\alpha)$ is a generalization of several other families of analytic functions available in literature.\n 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.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2021-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"92","ListUrlMain":"https://doi.org/10.34198/EJMS.7121.4976","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
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.
期刊介绍:
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