Inclusion relations of $ q $-Bessel functions associated with generalized conic domain

In this paper, we investigate the geometric properties of Jackson and Hahn-Exton q-Bessel functions and perform their normalization for the analyticity in open unit disk E. By applying normalized Jackson and Hahn-Exton q-Bessel functions and idea of convolution we introduce a new operator and define...

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Bibliographic Details
Published inAIMS mathematics Vol. 6; no. 4; pp. 3624 - 3640
Main Authors Khan, Shahid, Hussain, Saqib, Darus, Maslina
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
analytic functions
generalized conic domain ωk，q
q-bessel functions
q-calculus
q-convex functions
q-derivative
q-starlike functions
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Summary:In this paper, we investigate the geometric properties of Jackson and Hahn-Exton q-Bessel functions and perform their normalization for the analyticity in open unit disk E. By applying normalized Jackson and Hahn-Exton q-Bessel functions and idea of convolution we introduce a new operator and define new family of subclasses of analytic functions related with generalized conic domain. For these subclasses of analytic functions, we investigate inclusion relations and integral preserving properties. Also we will use q-Bernardi integral operator to discuss some applications of our main results.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021216