Applications of the Symmetric Quantum-Difference Operator for New Subclasses of Meromorphic Functions

Our goal in this article is to use ideas from symmetric q-calculus operator theory in the study of meromorphic functions on the punctured unit disc and to propose a novel symmetric q-difference operator for these functions. A few additional classes of meromorphic functions are then defined in light...

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Bibliographic Details
Published inSymmetry (Basel) Vol. 15; no. 7; p. 1439
Main Authors Al-shbeil, Isra, Khan, Shahid, AlAqad, Hala, Alnabulsi, Salam, Khan, Mohammad Faisal
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.07.2023
Subjects
Calculus
Convex analysis
Finite differences
Mathematical analysis
Meromorphic functions
meromorphic q-convex functions
meromorphic q-starlike functions
Operators (mathematics)
Physics
subordination
symmetric q-calculus
symmetric q-derivative operator
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Summary:Our goal in this article is to use ideas from symmetric q-calculus operator theory in the study of meromorphic functions on the punctured unit disc and to propose a novel symmetric q-difference operator for these functions. A few additional classes of meromorphic functions are then defined in light of this new symmetric q-difference operator. We prove many useful conclusions regarding these newly constructed classes of meromorphic functions, such as convolution, subordination features, integral representations, and necessary conditions. The technique presented in this article may be used to produce a wide variety of new types of generalized symmetric q-difference operators, which can subsequently be used to investigate a wide variety of new classes of analytic and meromorphic functions related to symmetric quantum calculus.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym15071439