$(p,q)$-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.

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

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