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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.
The first part of the paper is devoted to studying the continuous dependence of the solutions of Caratheodory constant delay differential equations where the vector fields satisfy classical cooperative conditions. As a consequence, when the set of co
We introduce new weak topologies and spaces of Caratheodory functions where the solutions of the ordinary differential equations depend continuously on the initial data and vector fields. The induced local skew-product flow is proved to be continuous
In this article, by making use of the linear operator introduced and studied by Srivastava and Attiya cite{srivastava1}, suitable classes of admissible functions are investigated and the dual properties of the third-order differential subordinations
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.
For $frac12<p<infty$, $0<q<infty$ and a certain two-sided doubling weight $omega$, we characterize those inner functions $Theta$ for which $$|Theta|_{A^{p,q}_omega}^q=int_0^1 left(int_0^{2pi} |Theta(re^{itheta})|^p dthetaright)^{q/p} omega(r),dr<in