New Criteria for Multivalently Meromorphic Convex Functions of Order Α Serap Bulut

Let J n+p−1 (α) (p ∈ N, n > −p, 0 α < p) denote the class of functions of the form f (z) = 1 z p + a 0 z p−1 + a 1 z p−2 + ··· which are regular and p-valent in the punctured unit disc U * = {z ∈ C : 0 < |z| < 1} and satisfy the condition Re (D n+p f (z)) (D n+p−1 f (z)) − (p + 1) < − p (n + p − 1) + α n + p , where D n+p−1 f (z) = 1 z p (1 − z) n+p * f (z). It is proved that J n+p (α) ⊂ J n+p−1 (α). Since J 0 (α) is the class of p-valently meromor-phic convex functions of order α (0 α < p) , all functions in J n+p−1 (α) are p-valently meromorphic convex of order α. Further, we consider the integral operators of functions in J n+p−1 (α).