Fekete-Szegő inequalities for certain class of analytic functions connected with q-analogue of Bessel function

Abstract

Abstract In this paper, we obtain Fekete-Szegő inequalities for a certain class of analytic functions f satisfying 1+1ζzNν,qλf(z)′(1−γ)Nν,qλf(z)+γzNν,qλf(z)′−1≺Ψ(z) $1+\frac {1}{\zeta }\left [\frac {z\left (\mathcal {N}_{\nu,q}^{\lambda }f(z)\right)^{\prime }} {(1-\gamma)\mathcal {N} _{\nu,q}^{\lambda }f(z)+\gamma z\left (\mathcal {N}_{\nu,q}^{\lambda }f(z) \right)^{\prime }}-1\right ]\prec \Psi (z)$. Application of our results to certain functions defined by convolution products with a normalized analytic function is given, and in particular, Fekete-Szegő inequalities for certain subclasses of functions defined through Poisson distribution are obtained.

Keywords

• Fekete-Szegő inequality
• Differential subordination
• Bessel function of first kind
• q-derivative
• Poisson distribution