Differential Subordinations: Theory and Applications

By Sanford S. Miller, P. Mocanu. 2000

1,106 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

On certain subclasses of multivalent functions associated with an extended fractional differintegral operator (2007, neutral): “, [10], see also [12]): f (z) ≺ g(z) (z ∈ U) ⇐⇒ f (0) = g(0) and f (U) ⊂ g(U).”
Coefficient estimates of new classes of q-starlike and q-convex functions of complex order (2016, background): “Furthermore, if the function g(z) is univalent in U , then we have the following equivalence holds (see [17] and [12]): f (z) ≺ g(z) ⇐⇒ f (0) = g(0) and f (U) ⊂ g(U).”
Third-order differential inequalities and subordinations in the complex plane (2011, background): “Slight variations of these two special cases played a crucial role in the development of first- and second-order differential subordinations as described extensively in [3,4].”
Starlikness Associated with Cosine Hyperbolic Function (2020, background): “For more details about differential subordinations, see [19].”
Inclusion Properties of Certain Subclasses of Analytic Functions (2012, background): “U z ∈ Furthermore, if the function g is univalent in U , then we have the following equivalence(See [4],[10] and [11]): ) 0 ( ) 0 ( g f g f = ⇔ p and ).”
Study on the q-analogue of a certain family of linear operators (2019, background): “1) Subordination of two functions f and g is denoted by f ≺ g and defined as f(z) = g(w(z)) , where w(z) is the Schwartz function in O (see [18]).”