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2017 Application of strong differential superordination to a general equation
R. Aghalary, P. Arjomandinia, A. Ebadian
Rocky Mountain J. Math. 47(2): 383-390 (2017). DOI: 10.1216/RMJ-2017-47-2-383

Abstract

In this paper, we study the notion of strong differential superordination as a dual concept of strong differential subordination, introduced in~\cite {1.a}. The notion of strong differential superordination has recently been studied by many authors, see, for example, \cite {2.a, 3.a, 5.a}. Let $q(z)$ be an analytic function in $\mathbb {D}$ that satisfies the first order differential equation $$\theta (q(z))+F(z)q'(z)\varphi (q(z))=h(z).$$ \smallskip Suppose that $p(z)$ is analytic and univalent in the closure of the open unit disk $\overline {\mathbb {D}}$ with $p(0)=q(0)$. We shall find conditions on $h(z),G(z),\theta (z)$ and $\varphi (z)$ such that $$ h(z)\prec \prec \theta (p(z))+\frac {G(\xi )}{\xi }zp'(z)\varphi (p(z))\Longrightarrow q(z)\prec p(z). $$ Applications and examples of the main results are also considered.

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R. Aghalary. P. Arjomandinia. A. Ebadian. "Application of strong differential superordination to a general equation." Rocky Mountain J. Math. 47 (2) 383 - 390, 2017. https://doi.org/10.1216/RMJ-2017-47-2-383

Information

Published: 2017
First available in Project Euclid: 18 April 2017

zbMATH: 1364.30017
MathSciNet: MR3635364
Digital Object Identifier: 10.1216/RMJ-2017-47-2-383

Subjects:
Primary: 30C45
Secondary: 30C80

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 2 • 2017
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