Applications of q-Derivative Operator to the Subclass of Bi-Univalent Functions Involving q-Chebyshev Polynomials

In recent years, the usage of the q-derivative and symmetric q-derivative operators is significant. In this study, firstly, many known concepts of the q-derivative operator are highlighted and given. We then use the symmetric q-derivative operator and certain q-Chebyshev polynomials to define a new...

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Bibliographic Details
Published inJournal of mathematics (Hidawi) Vol. 2022; no. 1
Main Authors Khan, Bilal, Liu, Zhi-Guo, Shaba, Timilehin Gideon, Araci, Serkan, Khan, Nazar, Khan, Muhammad Ghaffar
Format Journal Article
LanguageEnglish
Published Cairo Hindawi 2022
John Wiley & Sons, Inc
Wiley
Subjects
Applied mathematics
Calculus
Chebyshev approximation
Convex analysis
Functions (mathematics)
Mathematical analysis
Mathematics
Operators (mathematics)
Polynomials
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Summary:In recent years, the usage of the q-derivative and symmetric q-derivative operators is significant. In this study, firstly, many known concepts of the q-derivative operator are highlighted and given. We then use the symmetric q-derivative operator and certain q-Chebyshev polynomials to define a new subclass of analytic and bi-univalent functions. For this newly defined functions’ classes, a number of coefficient bounds, along with the Fekete–Szegö inequalities, are also given. To validate our results, we give some known consequences in form of remarks.
Bibliography:ObjectType-Article-1
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ISSN:2314-4629
2314-4785
DOI:10.1155/2022/8162182