Inclusion and Neighborhood Properties of Some Analytic and Multivalent Functions Associated with an Extended Fractional Differintegral Operator

By means of a certain extended fractional differintegral operator Ω (λ,p) z (−∞ < λ < p + 1; p ∈ N), the authors introduce and investigate two new subclasses of p-valently analytic functions of complex order. The various results obtained here for each of these function classes include coefficient inequalities and the consequent inclusion relationships involving the neighborhoods of the p-valently analytic functions. 2000 Mathematics Subject Classification: : 30C45. 1.Introduction, Definitions and Preliminaries Let Ap(n) denote the class of functions f(z) normalized by f(z) = z − ∞ ∑ k=n+p akz k (ak ≥ 0; n, p ∈ N := {1, 2, 3, ...}), (1) which are analytic and p-valent in the open unit disk U = {z : z ∈ C and |z| < 1} . Following the works of Goodman [4] , Ruscheweyh [12], Altintas et al. [3] and Raina and Srivastava [13], we define the (n, δ)− neigborhood of a function f(z) ∈ Ap(n) by (see also [2], [7] and [15]), Nn,δ(f) := { g(z) ∈ Ap(n) : g(z) = z − ∞ ∑