Certain subclass of analytic functions based on $ q $-derivative operator associated with the generalized Pascal snail and its applications

Abstract

<abstract><p>By the principle of differential subordination and the $ q $-derivative operator, we introduce the $ q $-analog $ \mathcal{SP}^{q}_{snail}(\lambda; \alpha, \beta, \gamma) $ of certain class of analytic functions associated with the generalized Pascal snail. Firstly, we obtain the coefficient estimates and Fekete-Szegö functional inequalities for this class. Meanwhile, we also estimate the corresponding symmetric Toeplitz determinant. Secondly, for all the above results we provide the corresponding results for the reduced classes $ \mathcal{SP}^{q}_{snail}(\alpha, \beta, \gamma) $ and $ \mathcal{RP}^{q}_{snail}(\alpha, \beta, \gamma) $. Thirdly, we characterize the Bohr radius problems for the function class $ \mathcal{SP}^{q}_{snail}(\alpha, \beta, \gamma) $. Lastly, we establish certain results for some new subclasses of functions defined by the neutrosophic Poisson distribution series.</p></abstract>