On Dual Sets and Neighborhood of New Subclasses of Analytic Functions Involving q-Derivative

Abstract

Quantum theory has wide applications in special functions and quantum physics. In this paper, we discuss the geometric properties of analytic functions using q-differential operator. We introduce some new subclasses of analytic functions which are obtained from the q-derivative and conic domains. We investigate interesting results involving dual sets and convolution properties of these new subclasses. We also study the inclusion properties of neighborhood of analytic functions. Our results continue to hold for the known and new subclasses of analytic functions which can be obtained as special case.