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2022 | OriginalPaper | Chapter

Extensions of Some Known Differential and Integral Operators

Author : Georgia Irina Oros

Published in: Mathematical, Computational Intelligence and Engineering Approaches for Tourism, Agriculture and Healthcare

Publisher: Springer Singapore

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Abstract

In this paper, the operator \(L^{m}:A\rightarrow A\) is introduced by \(L^{m}[f](z)=(1-\lambda )R^{m}[f](z)+\lambda I^{m}[f](z)\), \(z\in U\), a differential–integral operator where \(R^{m}\) is Ruscheweyh differential operator and \(I^{m}\) is Alexander integral operator. By using the operator \(L^{m}\) the class denoted by \(M^{m}(\lambda ,\beta )\), \(0\le \lambda \le 1\) , \(0\le \beta <1\) is defined. Using the operator \(L^{m}\), several differential subordinations are studied and from this study we obtain a condition for univalence of functions from class A.

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Metadata
Title
Extensions of Some Known Differential and Integral Operators
Author
Georgia Irina Oros
Copyright Year
2022
Publisher
Springer Singapore
Book
Mathematical, Computational Intelligence and Engineering Approaches for Tourism, Agriculture and Healthcare

Print ISBN: 978-981-16-3806-0

Electronic ISBN: 978-981-16-3807-7

Copyright Year: 2022

DOI
https://doi.org/10.1007/978-981-16-3807-7_2

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