Some Applications of a First Order Differential Subordination
نویسندگان
چکیده
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 sufficient conditions for starlikeness and univalence of functions analytic in the unit disc E.
منابع مشابه
Strong differential subordination and superordination of analytic functions associated with Komatu operator
Strong dierential subordination and superordination properties are determined for some familiesanalytic functions in the open unit disk which are associated with the Komatu operator by investigatingappropriate classes of admissible functions. New strong dierential sandwich-type results arealso obtained.
متن کاملSubordination and Superordination Properties for Convolution Operator
In present paper a certain convolution operator of analytic functions is defined. Moreover, subordination and superordination- preserving properties for a class of analytic operators defined on the space of normalized analytic functions in the open unit disk is obtained. We also apply this to obtain sandwich results and generalizations of some known results.
متن کاملDifferential subordination and superordination results associated with the Wright function
An operator associated with the Wright function is introduced in the open unit disk. Differential subordination and superordination results associated with this operator are obtained by investigating appropriate classes of admissible functions. In particular, some inequalities for modified Bessel functions are also obtained.
متن کاملCertain Second Order Linear Differential Subordinations
In this present investigation, we obtain some results for certain second order linear differential subordination. We also discuss some applications of our results.
متن کاملSANDWICH THEOREMS FOR HIGHER-ORDER DERIVATIVES OF p-VALENT FUNCTIONS DEFINED BY CERTAIN LINEAR OPERATOR
In this paper, we obtain some applications of first order differential subordination and superordination results for higher-order derivatives of p-valent functions involving certain linear operator. Some of our results improve and generalize previously known results.
متن کاملApplications of subordination theory to starlike functions
Let $p$ be an analytic function defined on the open unit disc $mathbb{D}$ with $p(0)=1.$ The conditions on $alpha$ and $beta$ are derived for $p(z)$ to be subordinate to $1+4z/3+2z^{2}/3=:varphi_{C}(z)$ when $(1-alpha)p(z)+alpha p^{2}(z)+beta zp'(z)/p(z)$ is subordinate to $e^{z}$. Similar problems were investigated for $p(z)$ to lie in a region bounded by lemniscate of Bernoulli $|w^{2}-1|=1$ ...
متن کامل