On a first order strong differential subordination and application to univalent functions
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Using the concept of the strong differential subordination introduced in \cite{4.a}, we find conditions on the functions $\theta, \varphi, G, F$ such that the first order strong subordination $$\theta(p(z))+\frac{G(\xi)}{\xi} zp'(z)\varphi(p(z))\prec \prec \theta(q(z))+F(z)q'(z)\varphi(q(z),$$ implies $$p(z)\prec q(z),$$ where $p(z), q(z)$ are analytic functions in the open unit disk $\mathbb{D}$ with $p(0)=q(0)$. Corollaries and examples of the main results are also considered, some of which extend and improve the results obtained in \cite{1.a}.
Abstract
Using the concept of the strong differential subordination introduced in \cite{4.a}, we find conditions on the functions $\theta, \varphi, G, F$ such that the first order strong subordination $$\theta(p(z))+\frac{G(\xi)}{\xi} zp'(z)\varphi(p(z))\prec \prec \theta(q(z))+F(z)q'(z)\varphi(q(z),$$ implies $$p(z)\prec q(z),$$ where $p(z), q(z)$ are analytic functions in the open unit disk $\mathbb{D}$ with $p(0)=q(0)$. Corollaries and examples of the main results are also considered, some of which extend and improve the results obtained in \cite{1.a}.
참고문헌 (10)
- Jos\'e A. Antonino, "Strong differential subordination and applications to univalency conditions", 대한수학회지, 43(2), pp.311~322 (2006), 대한수학회
- J.A. Antonino, "Strong Differential Subordination to Briot-Bouquet Differential Equations", Journal of Differential Equations, 114(1), pp.101~105 (1994), Elsevier BV[DOI]
- T. Bulboacǎ, "On some classes of dierential subordinations", Stud. Univ. Babes-Bolyai Math, 31(1), pp.45~50 (1986)
- T. Bulboacǎ, "On some classes of dierential subordinations. II", Stud. Univ. Babes-Bolyai Math, 31(2), pp.13~21 (1986)
- T. Bulboacǎ, "On a dierential inequality for analytic functions", Mathematica (Cluj), 28(1), pp.21~25 (1986)
- Sanford S. Miller, "On some classes of first-order differential subordinations.", Michigan Mathematical Journal, 32(2), pp.185~195 (1985), Michigan Mathematical Journal[DOI]
- S. S. Miller, "Dierential subordinations" (2000), Marcel Dekker, Inc
- G. I. Oros, "First order linear strong dierential subordinations", Gen. Math, 15(2), pp.98~107 (2007)
- G. I. Oros, "Strong dierential subordination", Turkish J. Math, 33(3), pp.249~257 (2009)
- C. Pommerenke, "Vandenhoeck & Ruprecht" (1975), Vandenhoeck & Ruprecht