Neighborhoods of a certain family of multivalent functions with negative coefficients

By making use of the familiar concept of neighborhoods of analytic and p-valent functions, the authors prove coefficient bounds and distortion inequalities, and associated inclusion relations for the (n, δ)-neighborhoods of a family of multivalent functions with negative coefficients, which is defined by means of a certain nonhomogeneous Cauchy-Euler differential equation. Relevant connections of the various function classes investigated in this paper with those considered by earlier workers on the subject are also mentioned.