No abstract

In the present investigation, we introduce the subclasses $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\phi)$ and $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\delta)$ of \textit{m}-fold symmetric bi-univalent function class $\Sigma_m$, which are associated with the pseudo-starlike functions and defined in the open unit disk $\mathbb{U}$. Moreover, we obtain estimates on the initial coefficients $|b_{m+1}|$ and $|b_{2m+1}|$ for the functions belong to these subclasses and identified correlations with some of the earlier known classes.

In mathematics, physics, and engineering, orthogonal polynomials and special functions play a vital role in the development of numerical and analytical approaches. This field of study has received a lot of attention in recent decades, and it is gaining traction in current fields, including computational fluid dynamics, computational probability, data assimilation, statistics, numerical analysis, and image and signal processing. In this paper, using q-Hermite polynomials, we define a new subclass of bi-univalent functions. We then obtain a number of important results such as bonds for the initial coefficients of |a2|, |a3|, and |a4|, results related to Fekete–Szegö functional, and the upper bounds of the second Hankel determinant for our defined functions class.

No abstract

The q-derivative and Hohlov operators have seen much use in recent years. First, numerous well-known principles of the q-derivative operator are highlighted and explained in this research. We then build a novel subclass of analytic and bi-univalent functions using the Hohlov operator and certain q-Chebyshev polynomials. A number of coefficient bounds, as well as the Fekete–Szegö inequalities and the second Hankel determinant are provided for these newly specified function classes.