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Mathematics

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Turkish Journal of Mathematics

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2022

Coefficient estimates

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Application Of Gegenbauer Polynomials For Biunivalent Functions Defined By Subordination, Fethi̇ye Müge Sakar, Saqib Hussain, Ibrar Ahmad Jan 2022

Application Of Gegenbauer Polynomials For Biunivalent Functions Defined By Subordination, Fethi̇ye Müge Sakar, Saqib Hussain, Ibrar Ahmad

Turkish Journal of Mathematics

We present and investigate a new subclass of biunivalent functions by applying Gegenbouer polynomials in this paper. Also, we find nonsharp estimates on the first two coefficients $\left \vert b_{0}\right \vert $ and $% \left \vert b_{1}\right \vert $ for functions belonging to this subclass. Furthermore, the Fekete-Szegö inequality $\left \vert b_{1}-\eta b_{0}^{2}\right \vert $ for this subclass is obtained. We also point out some consequences of results.


$(P,Q)$-Chebyshev Polynomials For The Families Of Biunivalent Function Associating A New Integral Operator With $(P,Q)$-Hurwitz Zeta Function, Sarem H. Hadi, Maslina Darus Jan 2022

$(P,Q)$-Chebyshev Polynomials For The Families Of Biunivalent Function Associating A New Integral Operator With $(P,Q)$-Hurwitz Zeta Function, Sarem H. Hadi, Maslina Darus

Turkish Journal of Mathematics

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.