اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدDifferential Subordinations For Functions With Positive Real Part Using Admissibility Conditions
61
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Some sufficient conditions on certain constants which are involved in some first, second and third order differential subordinations associated with certain functions with positive real part like modified Sigmoid function, exponential function and Janowski function are obtained so that the analytic function p normalized by the condition p(0) = 1, is subordinate to Janowski function. The admissibility conditions for Janowski function are used as a tool in the proof of the results. As application, several sufficient conditions are also computed for Janowski starlikeness.
قيم البحث
اقرأ أيضاً
In this paper we prove a quaternionic positive real lemma as well as its generalized version, in case the associated kernel has negative squares for slice hyperholomorphic functions. We consider the case of functions with positive real part in the ha
lf space of quaternions with positive real part, as well as the case of (generalized) Schur functions in the open unit ball.
Let $n$ be a positive integer. Let $mathbf U$ be the unit disk, $pge 1$ and let $h^p(mathbf U)$ be the Hardy space of harmonic functions. Kresin and Mazya in a recent paper found the representation for the function $H_{n,p}(z)$ in the inequality $$|f
^{(n)} (z)|leq H_{n,p}(z)|Re(f-mathcal P_l)|_{h^p(mathbf U)}, Re fin h^p(mathbf U), zin mathbf U,$$ where $mathcal P_l$ is a polynomial of degree $lle n-1$. We find or represent the sharp constant $C_{p,n}$ in the inequality $H_{n,p}(z)le frac{C_{p,n}}{(1-|z|^2)^{1/p+n}}$. This extends a recent result of the second author and Markovic, where it was considered the case $n=1$ only. As a corollary, an inequality for the modulus of the $n-{th}$ derivative of an analytic function defined in a complex domain with the bounded real part is obtained. This result improves some recent result of Kresin and Mazya.
We study the smoothness of the Siciak-Zaharjuta extremal function associated to a convex body in $mathbb{R}^2$. We also prove a formula relating the complex equilibrium measure of a convex body in $mathbb{R}^n$ to that of its Robin indicatrix. The main tool we use are extremal ellipses.
In this article, we wish to establish some first order differential subordination relations for certain Carath{e}odory functions with nice geometrical properties. Moreover, several implications are determined so that the normalized analytic function
belongs to various subclasses of starlike functions.
In this paper we determine the region of variability for certain subclasses of univalent functions satisfying differential inequalities. In the final section we graphically illustrate the region of variability for several sets of parameters.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
