Bi-univalent functions of order \(\zeta\) connected with \((m,n)\)-Lucas polynomials
Authors
S. H. Hadi
- Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq.
- Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor Darul Ehsan, Malaysia.
M. Darus
- Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor Darul Ehsan, Malaysia.
T. Bulboacă
- Faculty of Mathematics and Computer Science, Babeș-Bolyai University, 400084 Cluj-Napoca, Romania.
Abstract
With the aid of the \(q\)-binomial coefficients and utilizing the convolution, we define a new \(q\)-convolution operator that helps us introduce two new families of bi-univalent functions. These classes are connected by subordination with a function \(\mathcal{G}_{m,n}\). We give upper bounds for the coefficients estimate \(|a_j| \ (j=2,3)\) of the functions that belong to these families, followed by some special cases. Moreover, we found estimates for the Fekete-Sezgö inequality for both of these families, followed by simple particular results. We emphasize that the defined convolution \(q\)-difference operator generalizes some other operators given by several authors. As an application of this study, Fekete-Sezgö inequalities for these classes of functions defined by Pascal distribution
are investigated.
Share and Cite
ISRP Style
S. H. Hadi, M. Darus, T. Bulboacă, Bi-univalent functions of order \(\zeta\) connected with \((m,n)\)-Lucas polynomials, Journal of Mathematics and Computer Science, 31 (2023), no. 4, 433--447
AMA Style
Hadi S. H., Darus M., Bulboacă T., Bi-univalent functions of order \(\zeta\) connected with \((m,n)\)-Lucas polynomials. J Math Comput SCI-JM. (2023); 31(4):433--447
Chicago/Turabian Style
Hadi, S. H., Darus, M., Bulboacă, T.. "Bi-univalent functions of order \(\zeta\) connected with \((m,n)\)-Lucas polynomials." Journal of Mathematics and Computer Science, 31, no. 4 (2023): 433--447
Keywords
- Bi-univalent function
- \(q\)-exponential function
- \((m,n)\)-Lucas polynomials
- Fekete-Sezgö inequality
- Pascal distribution
MSC
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