A first-order differential double subordination with applications

A first-order differential double subordination with applications

Let q1 and q2 belong to a certain class of normalized analytic univalent functions in the open unit disk of the complex plane. Sufficient conditions are obtained for normalized analytic functions p to satisfy the double subordination chain q1(z)≺ p(z)≺ q2(z). The differential sandwich-type result obtained is applied to normalized univalent functions and to Φ-like functions.

Some Applications of a First Order Differential Subordination

Let p and q be analytic functions in the unit disc E = {z : |z| < 1}, with p(0) = q(0) = 1. Assume that α and δ are real numbers such that 0 < δ ≤ 1, α+ δ ≥ 0. Let β and γ be complex numbers with β 6= 0. In the present paper, we investigate the differential subordination (p(z)) [ p (z) + zp′(z) βp(z) + γ ]δ ≺ (q(z)) [ q(z) + zq′(z) βq(z) + γ ]δ , z ∈ E, and as applications, find several suffici...

Some applications of differential subordination

A number of interesting criteria were given by earlier workers for a normalized analytic function to be in the familiar class ∗ of starlike functions. The main object of the present paper is to extend and improve each of these earlier results. An application associated with an integral operator c(c >−1) is also considered.

A method for solving first order fuzzy differential equation

Subordination Principle for a Class of Fractional Order Differential Equations

The fractional order differential equation u′(t) = Au(t) + γD t Au(t) + f(t), t > 0, u(0) = a ∈ X is studied, whereA is an operator generating a strongly continuous one-parameter semigroup on a Banach space X , D t is the Riemann–Liouville fractional derivative of order α ∈ (0, 1), γ > 0 and f is an X-valued function. Equations of this type appear in the modeling of unidirectional viscoelastic ...