Subclasses of analytic and bi-univalent functions involving a generalized Mittag-Leffler function based on quasi-subordination

Volume 26, Issue 4, pp 379--394
Publication Date: January 06, 2022 Submission Date: September 29, 2021 Revision Date: November 07, 2021 Accteptance Date: December 02, 2021
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Authors

P. Long - School of Mathematics and Statistics, Ningxia University, Yinchuan, Ningxia 750021, People's Republic of China. G. Murugusundaramoorthy - Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, India. H. Tang - School of Mathematics and Computer Sciences, Chifeng University, Chifeng, Inner Mongolia 024000, People's Republic of China. W. Wang - School of Mathematics and Statistics, Ningxia University, Yinchuan, Ningxia 750021, People's Republic of China.

Abstract

Two quasi-subordination subclasses $\mathcal{Q}\Sigma^{\gamma,k}_{ \alpha,\beta}(\vartheta,\rho;\phi)$ and $\mathcal{M}\Sigma^{\gamma,k}_{ \alpha,\beta}(\tau,\vartheta,\rho;\phi)$ of the class $\Sigma$ of analytic and bi-univalent functions associated with the convolution operator involving Mittag-Leffler function are introduced and investigated. Then, the corresponding bound estimates of the coefficients $a_2$ and $a_3$ are provided. Meanwhile, Fekete-Szegö functional inequalities for these classes are proved. Besides, some consequences and connections to all the theorems would be interpreted, which generalize and improve earlier known results.

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ISRP Style

P. Long, G. Murugusundaramoorthy, H. Tang, W. Wang, Subclasses of analytic and bi-univalent functions involving a generalized Mittag-Leffler function based on quasi-subordination, Journal of Mathematics and Computer Science, 26 (2022), no. 4, 379--394

AMA Style

Long P., Murugusundaramoorthy G., Tang H., Wang W., Subclasses of analytic and bi-univalent functions involving a generalized Mittag-Leffler function based on quasi-subordination. J Math Comput SCI-JM. (2022); 26(4):379--394

Chicago/Turabian Style

Long, P., Murugusundaramoorthy, G., Tang, H., Wang, W.. "Subclasses of analytic and bi-univalent functions involving a generalized Mittag-Leffler function based on quasi-subordination." Journal of Mathematics and Computer Science, 26, no. 4 (2022): 379--394

Keywords

• Fekete-Szegö inequality
• bi-univalent function
• Mittag-Leffler function
• quasi-subordination

•  30C45
•  30C50
•  30C80