$(p,q)$-Chebyshev polynomials for the families of biunivalent function associating a new integral operator with $(p,q)$-Hurwitz zeta function

Authors

SAREM H. HADI
MASLINA DARUS

Abstract

In the present article, making use of the $(p,q)$-Hurwitz zeta function, we provide and investigate a new integral operator. Also, we define two families ${\mathcal{S}\mathcal{M}}_{p,q}\left(\xi ,\zeta,\delta,u,\tau \right)$ and ${\mathcal{S}\mathcal{C}}_{p,q}\left(\lambda, \zeta,\vartheta,u,\tau \right)$ of biunivalent and holomorphic functions in the unit disc connected with $(p,q)$-Chebyshev Polynomials. Then we find coefficient estimates $\left a_2\right $ and $\left a_3\right .$ Finally, we obtain Fekete-Szeg$\ddot{\mathrm{o}}$ inequalities for these families.

DOI

10.55730/1300-0098.3277

Keywords

Biunivalent function, $(p, q)$-Chebyshev polynomial, $(p, q)$-Hurwitz zeta function, a new integral operator, coefficient estimates, and Fekete-Szeg$\ddot{\mathrm{o}}$ inequality

First Page

2415

Last Page

2429

Recommended Citation

HADI, S. H, & DARUS, M (2022). $(p,q)$-Chebyshev polynomials for the families of biunivalent function associating a new integral operator with $(p,q)$-Hurwitz zeta function. Turkish Journal of Mathematics 46 (6): 2415-2429. https://doi.org/10.55730/1300-0098.3277