Abstract
In this paper, we derive some applications of first order differential subordination and superordination results involving Frasin operator for analytic functions in the open unit disk. Also by these results, we obtain sandwich results. Our results extend corresponding previously known results.
Highlights
Let H = H (U ) indicate the class of analytic functions in the open unit disk U = {z ∈ C : z < 1} and let H[a, n] be the subclass of H consisting of functions of the form: f (z) = a + an zn + an+1zn+1 + ⋯ (a ∈ C, n ∈ N = {1, 2, ...})
Let A be the subclass of H containing of functions of the form:
It is well known that, if the function g is univalent in U, f ≺ g if and only if f (0) = g(0) and f (U ) ⊂ g(U )
Summary
It is well known that, if the function g is univalent in U, f ≺ g if and only if f (0) = g(0) and f (U ) ⊂ g(U ). If ξ and ψ(ξ(z), zξ′(z), z2ξ′′(z); z) are univalent functions in U and if ξ satisfies the second-order differential superordination h(z) ≺ ψ(ξ(z), zξ′(z), z2ξ′′(z); z), (1.2) An analytic function q is called a subordinant of (1.2), if q ≺ ξ for all ξ satisfying (1.2).
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