"In this paper, we introduce new class $\Sigma_{m}(\mu,\lambda,\gamma,\beta)$ of $m$-fold symmetric bi-univalent functions. Furthermore, use the Faber polynomial expansions to find upper bounds for general coefficients $|a_{mk+1}|(k \geqq 2)$ functions in $\Sigma_{m}(\mu,\lambda,\gamma,\beta)$. Moreover, obtain estimates initial $|a_{m+1}| $ and $|a_{2m+1}|$ class. The results presented paper w...

Using the Al-Oboudi type operator, we present and investigate two special families of bi-univalent functions connected with activation function \(% \phi (s)=\ 2/(1+e^{-s}),\,s\in \mathbb{R}\) \(k\)-Fibonacci numbers. We derive bounds on initial coefficients Fekete-Szego functional for \(g_{\phi }(z)=z+\sum \limits_{j=2}^{\infty }\phi (s)d_{j}z^{j}\) in these introduced families. Furthermore, in...

Inspired by the recent works of Srivastava et al. (2010), Frasin and Aouf (2011), Caglar (2013), we introduce investigate in present paper two new general subclasses class consisting normalized analytic bi-univalent functions open unit disk U. For belonging to these introduced here, obtain estimates on Taylor-Maclaurin coefficients |a_2| |a_3|. Several connections some earlier known results are...

In this research, a novel linear operator involving the Borel distribution and Mittag-Leffler functions is introduced using Hadamard products or convolutions. This utilized to develop new subfamilies of bi-univalent via principle subordination with Gegenbauer orthogonal polynomials. The investigation also focuses on estimation coefficients |a?|(?=2,3) Fekete–Szegö inequality for belonging these...