In the present article, certain classes of generalized p-valent Robertson functions are considered. Mapping properties of these classes are investigated under certain p-valent integral operators introduced by Frasin recently.

Let T (n, p) denote the class of functions of the form f (z) = z p − ∑ ∞ k=n ak+pz k+p (ak+p ≥ 0; p, n ∈ N ) which are analytic and p-valent in the open unit disc U = {z : |z| < 1}. For functions f j (z) ( j = 1, 2) belonging to T (n, p), generalizations of the modified-Hadamard product of f1(z) and f2(z) represented by ( f1∆ f2) (r, s; z) (r, s ∈ R) are introduced. In this paper, we obtain sev...

Let M be a Riemannian manifold. For p ∈ M , the tensor algebra of the negative part of the (complex) affinization of the tangent space of M at p has a natural structure of a meromorphic open-string vertex algebra. These meromorphic open-string vertex algebras form a vector bundle over M with a connection. We construct a sheaf V of meromorphic open-string vertex algebras on the sheaf of parallel...

In this paper, we investigate the relationship between solutions and their derivatives of the differential equation f (k) + A(z)f = 0, k ≥ 2, where A(z) is a transcendental meromorphic function with ρp(A) = ρ > 0 and meromorphic functions of finite iterated p−order.