Upper bound for the second and third Hankel determinants of analytic functions associated with the error function and q-convolution combination

Abstract

Abstract Recently, El-Deeb and Cotîrlă (Mathematics 11:11234834, 2023) used the error function together with a q-convolution to introduce a new operator. By means of this operator the following class R α , ϒ λ , q ( δ , η ) $\mathcal{R}_{\alpha ,\Upsilon}^{\lambda ,q}(\delta ,\eta )$ of analytic functions was studied: R α , ϒ λ , q ( δ , η ) : = { F : ℜ ( ( 1 − δ + 2 η ) H ϒ λ , q F ( ζ ) ζ + ( δ − 2 η ) ( H ϒ λ , q F ( ζ ) ) ′ + η ζ ( H ϒ λ , q F ( ζ ) ) ″ ) } > α ( 0 ≦ α \alpha \quad (0\leqq \alpha < 1). \end{aligned}$$ For these general analytic functions F ∈ R β , ϒ λ , q ( δ , η ) $\mathcal{F}\in \mathcal{R}_{\beta ,\Upsilon}^{\lambda ,q}(\delta , \eta )$ , we give upper bounds for the Fekete–Szegö functional and for the second and third Hankel determinants.

Keywords

• Hankel determinant
• Analytic functions
• Error function
• Convolution
• q-Derivative operator
• Coefficient inequalities