Neighborhood properties of certain classes of multivalently analytic functions associated with the convolution structure

Keywords: Analytic functions Starlike and convex functions Multivalent functions Hadamard product (or convolution) Coefficient bounds Distortion inequalities Neighborhood properties Non-homogeneous Cauchy–Euler differential equations a b s t r a c t In this paper, by making use of the familiar concept of neighborhoods of p-valently analytic functions, we prove coefficient bounds, distortion inequalities and associated inclusion relations for the (n, d)-neighborhoods of a family of p-valently analytic functions and their derivatives, which is defined by means of a certain general family of non-homogenous Cau-chy–Euler differential equations.