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Faber polynomial coefficient estimates of bi-univalent functions connected with the $q$ -convolution

Sheza M. El-Deeb; Serap Bulut — 2023

Mathematica Bohemica

We introduce a new class of bi-univalent functions defined in the open unit disc and connected with a $q$ -convolution. We find estimates for the general Taylor-Maclaurin coefficients of the functions in this class by using Faber polynomial expansions and we obtain an estimation for the Fekete-Szegö problem for this class.

Fuzzy differential subordinations connected with the linear operator

Sheza M. El-Deeb; Georgia I. Oros — 2021

Mathematica Bohemica

We obtain several fuzzy differential subordinations by using a linear operator $ℐ_{m, γ}^{n, α} f (z) = z + \sum_{k = 2}^{\infty} {(1 + γ (k - 1))}^{n} m^{α} {(m + k)}^{- α} a_{k} z^{k}$ . Using the linear operator $ℐ_{m, γ}^{n, α},$ we also introduce a class of univalent analytic functions for which we give some properties.

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Faber polynomial coefficient estimates of bi-univalent functions connected with the q -convolution

Fuzzy differential subordinations connected with the linear operator

Faber polynomial coefficient estimates of bi-univalent functions connected with the $q$ -convolution