Certain Subclasses of Analytic Multivalent Functions Associated with Petal-Shape Domain

In this article, we introduce a new class of multivalent analytic functions associated with petal-shape region. Furthermore, some useful properties, such as the Fekete–Szegö inequality, and their consequences for some special cases are discussed. For some specific value of function <i>f</i&...

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Bibliographic Details
Main Authors: Lei Shi, Hari M. Srivastava, Muhammad Ghaffar Khan, Nazar Khan, Bakhtiar Ahmad, Bilal Khan, Wali Khan Mashwani
Format: Article
Language:English
Published: MDPI AG 2021-11-01
Series:Axioms
Subjects:
Online Access:https://www.mdpi.com/2075-1680/10/4/291
Description
Summary:In this article, we introduce a new class of multivalent analytic functions associated with petal-shape region. Furthermore, some useful properties, such as the Fekete–Szegö inequality, and their consequences for some special cases are discussed. For some specific value of function <i>f</i>, we obtain sufficient conditions for multivalent starlike functions connected with petal-shape domain. Finally, in the concluding section, we draw the attention of the interested readers toward the prospect of studying the basic or quantum (or <i>q</i>-) generalizations of the results, which are presented in this paper. However, the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><mi mathvariant="fraktur">p</mi><mo>,</mo><mi>q</mi><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula>-variations of the suggested <i>q</i>-results will provide a relatively minor and inconsequential development because the additional (rather forced-in) parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">p</mi></semantics></math></inline-formula> is obviously redundant.
ISSN:2075-1680