APPLICATION OF STRONG DIFFERENTIAL SUPERORDINATION TO A GENERAL EQUATION

作者：Aghalary R^*; Arjomandinia P; Ebadian A

来源：Rocky Mountain Journal of Mathematics, 2017, 47(2): 383-390.

DOI：10.1216/RMJ-2017-47-2-383

• Convex
• univalent and starlike function
• strong differential superordination

In this paper, we study the notion of strong differential superordination as a dual concept of strong differential subordination, introduced in [1]. The notion of strong differential superordination has recently been studied by many authors, see, for example, [2, 3, 5]. Let q(z) be an analytic function in (D) over bar that satisfies the first order differential equation
theta(q(z)) + F(z)q' (z)phi(q(z)) = h(z).
Suppose that p(z) is analytic and univalent in the closure of the open unit disk D with p(0) = q(0). We shall find conditions on h(z), G(z), theta(z) and phi(z) such that
h(z) << theta(p(z)) + G(xi)/xi zp' (z)phi(p(Z)) double right arrow q(z) < p(z).
Applications and examples of the main results are also considered.

• 出版日期2017