Further, these subordination results immediately give sufficient conditions for an analytic function $f$ to be in various well-known subclasses of starlike functions.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:For an analytic function $p$ satisfying $p(0)=1$, we obtain sharp estimates on $\beta$ such that the first order differential subordination $p(z)+\beta zp'(z)\prec \mathcal{P}(z)$ or $1+\beta zp'(z)/p^{j}(z)\prec \mathcal{P}(z)$, $(j=0,1,2)$ implies $p(z)\prec \mathcal{Q}(z)$ where $\mathcal{P}$ and $\mathcal{Q}$ are Carathéodory functions.
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Temel Bulgular & Veri:The key tools in the proof of main results are the theory of differential subordination and some properties of hypergeometric functions.
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Sonuç & Katkı:Further, these subordination results immediately give sufficient conditions for an analytic function $f$ to be in various well-known subclasses of starlike functions.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:differential subordination · starlike function · lemniscate of Bernoulli
Abstract
For an analytic function $p$ satisfying $p(0)=1$, we obtain sharp estimates on $\beta$ such that the first order differential subordination $p(z)+\beta zp'(z)\prec \mathcal{P}(z)$ or $1+\beta zp'(z)/p^{j}(z)\prec \mathcal{P}(z)$, $(j=0,1,2)$ implies $p(z)\prec \mathcal{Q}(z)$ where $\mathcal{P}$ and $\mathcal{Q}$ are Carathéodory functions. The key tools in the proof of main results are the theory of differential subordination and some properties of hypergeometric functions. Further, these subordination results immediately give sufficient conditions for an analytic function $f$ to be in various well-known subclasses of starlike functions.
Bohra, N., Kumar, S., Ravichandran, V. (2022). Some special differential subordinations. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 4, 1017–1034. https://ajindex.com/articles/530150
R. Aghalary, P. Arjomandinia and A. Ebadian, Application of strong differential superordination to a general equation, Rocky Mountain J. Math. 47 (2), 383-390, 2017
R.M. Ali, N.E. Cho, V. Ravichandran and S.S. Kumar, Differential subordination for functions associated with the lemniscate of Bernoulli, Taiwanese J. Math. 16 (3), 1017-1026, 2012
R.M. Ali, V. Ravichandran and N. Seenivasagan, Sufficient conditions for Janowski starlikeness, Int. J. Math. Math. Sci. 2007, Art. ID 62925, 7 pages, 2007
O. Altintas, Certain applications of subordination associated with neighborhoods, Hacet. J. Math. Stat. 39 (4), 527-534, 2010
N. Bohra and V. Ravichandran, On Confluent hypergeometric function and generalized Bessel functions, Anal. Math. 43 (4), 533-545, 2017
T. Bulboacă, Differential Subordinations and Superordinations. Recent Results, House of Scientific Book Publ., Cluj-Napoca, 2005
T. Bulboacă, N.E. Cho and P. Goswami, Differential superordinations and sandwichtype results, in: Current Topics in Pure and Computational Complex Analysis, 109- 146, Trends Math, Birkhäuser/Springer, New Delhi, 2014
N.E. Cho, V. Kumar, S.S. Kumar and V. Ravichandran, Radius Problems for Starlike Functions Associated with the Sine Function, Bull. Iranian Math. Soc. 45 (1), 213-232, 2019
P.L. Duren, Univalent Functions, GTM 259, Springer-Verlag, New York, 1983
I. Faisal and M. Darus, Application of nonhomogenous Cauchy-Euler differential equation for certain class of analytic functions, Hacet. J. Math. Stat. 43 (3), 375-382, 2014
A.W. Goodman, Univalent Functions. Vol. I, Mariner, Tampa, FL, 1983
P. Hästö, S. Ponnusamy and M. Vuorinen, Starlikeness of the Gaussian hypergeometric functions, Complex Var. Elliptic Equ. 55 (1-3), 173-184, 2010
W. Janowski, Some extremal problems for certain families of analytic functions. I, Ann. Polon. Math. 28, 297-326, 1973
S.S. Kumar, V. Kumar, V. Ravichandran and N.E. Cho, Sufficient conditions for starlike functions associated with the lemniscate of Bernoulli, J Inequal. Appl. 2013, Art. ID 176, 13 pages, 2013
S. Kumar and V. Ravichandran, A subclass of starlike functions associated with a rational function, Southeast Asian Bull. Math. 40 (2), 199-212, 2016
S. Kumar and V. Ravichandran, Subordinations for functions with positive real part, Complex Anal. Oper. Theory 12 (5), 1179-1191, 2018
W.C. Ma and D. Minda, A unified treatment of some special classes of