TY - JOUR T1 - SOME INEQUALITIES FOR POLYNOMIAL FUNCTIONS TT - POLİNOM FONKSİYONLAR İÇİN BAZI EŞİTSİZLİKLER AU - Çelik, Adem PY - 2013 DA - March DO - 10.12739/NWSA.2013.8.2.3A0064 JF - Physical Sciences PB - E-Journal of New World Sciences Academy WT - DergiPark SN - 1308-7304 SP - 32 EP - 47 VL - 8 IS - 2 LA - tr AB - 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. KW - Mathematicle Analysis KW - Polynomial Functions KW - Univalent Function with Three Preassigned Values KW - Maximum Modulus Values KW - Inequalities KW - N2 - 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. CR - Ankeny, N.C. and Rivlin, T.J., (1955). On a theorem of S. Brenstein, Pasific J. Math., 849-852. CR - Avcı, Y. and Zlotkiewicz, E., (1997). On univalent functions with three preassigend values, Tr. J. of Mathematics, 21, 15-23. CR - Çelik, A., (2012). New inequalities for Maximum Modulus Values of polynomial functions, Hacettepe Journal of Mathematics and Statistics, volume 41 (2), 255-263. CR - 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. CR - Çelik, A., (2004). Maximum module values of polynomials on z R (R CR - 1), Üniv. Beograd, publ. Elektrotehn. Fak.,ser. Mat.15,1-6. CR - Çelik, A., (1997). A note on Mohr’s paper, Üniv. Beograd, publ. Elektrotehn. Fak.,ser. Mat.8, 51-54. CR - Deshpande, J.V., (1986). Complex Analysis, Tata MCGraw-Hill Publising Company, New Delhi. CR - Duren, P.L., (1983). Univalent functions Newyork-Berlin, Springer Verlag. CR - Milonovic’ G.V., Mitrinovic’ D.S., and Rassias, M.TH., (1994). Extremal Problems, Inequalities Zeros ,Word Scientific Publ. Co., Singapore, New Jersey, London. CR - Mir, A., Devan, K.K., and Sing, N., (2009). Some inequalities concerning The rate of growty of polinomials, Turk. J. Math., 33, 239-247. CR - 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. CR - 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. CR - Rassias, M.TH., (1986). A new inequality for complex-valued polynomial functions, Proc. Amer. Math. Soc. 9, 296-298. UR - https://doi.org/10.12739/NWSA.2013.8.2.3A0064 L1 - https://dergipark.org.tr/en/download/article-file/186939 ER -