New criteria for multivalently meromorphic convex functions of order α
Journal of Classical Analysis
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 and satisfy the condition is the class of p -valently meromorphic 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). which are regular and p -valent in the punctured unit
... punctured unit disc Mathematics subject classification (2010): 30C45. Various special cases of the class J n+p−1 (α) were considered by many earlier researchers on this topic of Geometric Function Theory. For example, we have the following relationships with the classes which were studied in some of these earlier works: In this paper, it is proved that the class J n+p−1 (α) consisting of functions in Σ p satisfying (1.1) holds the relationship Since J 0 (α) = M K p (α), it follows from (1.2) that all functions in J n+p−1 (α) are p -valently meromorphic convex of order α.