Abstract
Bu çalışmada, önce ,12, de birim diskte polinomların maksimum modülleri için ispatlanan eşitsizliğin, herhangi bir R yarıçaplı disk için de geçerli olduğu gösterildi. z=0 noktası polinomların katlı kökü olması durumunda , ve f(0)=0 , f(a)=a^q,f(-a)=-a^q olan f:C---C ünivalent polinomlar için, bu eşitsizliğin farklı formları elde edilmiştir. Ayrıca ,ünivalent polinom fonksiyonlar için bu eşitsizliklerden tamamen farklı yeni eşitsizlikler hem birim diskte hem de herhangi bir R yarıçaplı bir diskte elde edilmiştir.
Keywords
Matematiksel Analiz Polinom Fonksiyonlar Ön Görülen Üç Değeri Alan Ünivalent Fonksiyonlar Maksimum Modül Değerler Eşitsizlikler
References
- Ankeny, N.C. and Rivlin, T.J., (1955). On a theorem of S. Brenstein, Pasific J. Math., 849-852.
- Avcı, Y. and Zlotkiewicz, E., (1997). On univalent functions with three preassigend values, Tr. J. of Mathematics, 21, 15-23.
- Çelik, A., (2012). New inequalities for Maximum Modulus Values of polynomial functions, Hacettepe Journal of Mathematics and Statistics, volume 41 (2), 255-263.
- Çelik, A., (2009). On the “univalent functions with three preassigend Values and automorphisms of an open disc”,E-Journal New World Sciences Academy,volume 4,number 2, 36-41.
- Çelik, A., (2004). Maximum module values of polynomials on z R (R
- 1), Üniv. Beograd, publ. Elektrotehn. Fak.,ser. Mat.15,1-6.
- Çelik, A., (1997). A note on Mohr’s paper, Üniv. Beograd, publ. Elektrotehn. Fak.,ser. Mat.8, 51-54.
- Deshpande, J.V., (1986). Complex Analysis, Tata MCGraw-Hill Publising Company, New Delhi.
- Duren, P.L., (1983). Univalent functions Newyork-Berlin, Springer Verlag.
- Milonovic’ G.V., Mitrinovic’ D.S., and Rassias, M.TH., (1994). Extremal Problems, Inequalities Zeros ,Word Scientific Publ. Co., Singapore, New Jersey, London.
- Mir, A., Devan, K.K., and Sing, N., (2009). Some inequalities concerning The rate of growty of polinomials, Turk. J. Math., 33, 239-247.
- Mohr, E., (1992). Bemerkung Zu der arbeit Van A.M. Ostrowski Notiz uber Maximalwerte von polynomen auf dem einheitskreis Üniv. Beograd, publ. Elektrotehn.Fak,ser. Mat.3, 3-4.
- Ostrowski, A.M., (1979). Notiz uber Maximalwerte von polynomen auf dem einheitskreis, Üniv. Beograd, publ.Elektrotehn. Fak., ser. Mat. Fiz.,No 634-637, 55-56.
- Rassias, M.TH., (1986). A new inequality for complex-valued polynomial functions, Proc. Amer. Math. Soc. 9, 296-298.
Abstract
In this work, we first show that the inequality, established in the unit disc for maximum modulus of polynomial functions ,12, also holds for any disc of radius R . In the case where polynomials have z=0 as a multiple root, and also for the univalent polynomial functions f:C---C with f(0)=0 ,f(a=a^q , f(-a) =-a^q ,we obtain different forms of this inequality. Then we attain quite distinct new inequalities for univalent polynomial functions in both the unit disc and disc of an arbitrary radius R.
Keywords
Mathematicle Analysis Polynomial Functions Univalent Function with Three Preassigned Values Maximum Modulus Values Inequalities
References
- Ankeny, N.C. and Rivlin, T.J., (1955). On a theorem of S. Brenstein, Pasific J. Math., 849-852.
- Avcı, Y. and Zlotkiewicz, E., (1997). On univalent functions with three preassigend values, Tr. J. of Mathematics, 21, 15-23.
- Çelik, A., (2012). New inequalities for Maximum Modulus Values of polynomial functions, Hacettepe Journal of Mathematics and Statistics, volume 41 (2), 255-263.
- Çelik, A., (2009). On the “univalent functions with three preassigend Values and automorphisms of an open disc”,E-Journal New World Sciences Academy,volume 4,number 2, 36-41.
- Çelik, A., (2004). Maximum module values of polynomials on z R (R
- 1), Üniv. Beograd, publ. Elektrotehn. Fak.,ser. Mat.15,1-6.
- Çelik, A., (1997). A note on Mohr’s paper, Üniv. Beograd, publ. Elektrotehn. Fak.,ser. Mat.8, 51-54.
- Deshpande, J.V., (1986). Complex Analysis, Tata MCGraw-Hill Publising Company, New Delhi.
- Duren, P.L., (1983). Univalent functions Newyork-Berlin, Springer Verlag.
- Milonovic’ G.V., Mitrinovic’ D.S., and Rassias, M.TH., (1994). Extremal Problems, Inequalities Zeros ,Word Scientific Publ. Co., Singapore, New Jersey, London.
- Mir, A., Devan, K.K., and Sing, N., (2009). Some inequalities concerning The rate of growty of polinomials, Turk. J. Math., 33, 239-247.
- Mohr, E., (1992). Bemerkung Zu der arbeit Van A.M. Ostrowski Notiz uber Maximalwerte von polynomen auf dem einheitskreis Üniv. Beograd, publ. Elektrotehn.Fak,ser. Mat.3, 3-4.
- Ostrowski, A.M., (1979). Notiz uber Maximalwerte von polynomen auf dem einheitskreis, Üniv. Beograd, publ.Elektrotehn. Fak., ser. Mat. Fiz.,No 634-637, 55-56.
- Rassias, M.TH., (1986). A new inequality for complex-valued polynomial functions, Proc. Amer. Math. Soc. 9, 296-298.
Details
| Primary Language | Turkish |
|---|---|
| Journal Section | Physics |
| Authors | |
| Publication Date | March 1, 2013 |
| Published in Issue | Year 2013 Volume: 8 Issue: 2 |