BİR FUL HİPERBOLİK BÖLGEDE EŞİTSİZLİKLER

Öz

D kompleks düzlemde sadece hiperbollerle sınırlı bir bölge ( bir ful hiperbolik bölge ) olsun. Bu bölgede f(0)=0, f(a)=a^q, f(-a)=-a^q olan 4m dereceli kompleks değerli ünivalent polinom fonksiyonların UT2,2^4P(a) sınıfı için maksimum modül eşitsizlikleri elde edilmiştir. Bu eşitsizliklerde katsayılar: Birincisi IaI ya bağlı olarak; bir diğeri polinomların sıfırlarına bağlı olarak, ve üçünçüsü IaI ya ve polinomların sıfırlarına bağlı olarak. Sonra bu ful hiperbolik bölgenin bir özel durumu ( Bir birim ful hiperbolik bölge) için eşitsizlikler elde edilmiştir.

Anahtar Kelimeler

• Matematik Analiz, Öngörülen Üç Değeri Alan Polinom Fonksiyon, Hiperbolik Bölge, Maksimum Modül Değerler, Eşitsizlikler,

INEQUALITIES IN A HIPERBOLICAL REGION

Öz

Let D (on complex plane) be a region bounded only by hyperbolas (a full hyperbolical region). In this region, we obtain the maximum modulus inequalities for the class UT2,2^4P(a) of univalent polynomial functions wth complex values of degree 4m, in which f(0)=0, f(a)=a^q, f(-a)=-a^q. The coefficients in these inequaities are obtained by three distinct ways: The firs is depending on IaI; the other one is depending on the zeros of polynomials, and the third is depending on IaI and on the zeros of polynomials. Then we obtain inequalities for the special case where our region is unit full hyperbolical region.

Anahtar Kelimeler

• Mathematical Analysis, Polynomials Functions with Three Preasigned Values, Hiperbolical Region, Maximum Modulus Values, Inequalities,

Kaynakça

1. Ankeny, N.C. and Rivlin, T.J., (1955). On a theorem of S. Brenstein, Pasific J. Math., ss:849-852.
2. Aziz, A., (1987). Growty of polynomials whose zeros are within or outside a circle,Bull.Austral.Math. Soc. Vol.35, ss:247-256. Çelik, A., (2013). Inequalities for polynomial functions, NWSAPhysical Sciences, Volume: 8, Number: 2, ss:32-47.
3. DOI URL http://dx.doi.org/10.12739/NWSA.2013.8.4.3A0064
4. Çelik, A., (2012). New inequalities for Maximum Modulus Values of polynomial functions, Hacettepe Journal of Mathematics and Statistics, Volume: 41 (2), ss:255-263.
5. Çelik, A., (2009). On the ünivalent functions with three preasigned values and automorphism of an open disk, NWSAPhysical Sciences, Volume: 4, Number: 1, ss:36-41,2009.
6. Çelik, A., (2004). Maximum module values of polynomials on R z  ( ) 1  R , Üniv. Beograd, publ. Elektrotehn. Fak.,ser.Mat.15,ss:1-6 Çelik, A., (1997). A note on Mohr’s paper, Üniv.Beograd,publ. Elektrotehn. Fak., ser. Mat.8, ss: 51-54
7. Deshpande, J.V., (1986). Complex Analysis (Tata MCGraw-Hill Publising Company, New Delhi).
8. Dewan, K.K. and Ahuja, A., (2011). Growty of polynomials havings zeros inside a circle, Int. Journal of Math. Analysis, Volume:5, no.11, ss:499-505.

9. Gardner, R.B., (2004). Some results conserning rate of Growty of polynomials, East Journal on approximations, Volume: l0, Number: 3, ss:301-312.
10. Gardner, R.B., Govil, N.K., and Musukula, S.R., (2005). Rate of Growty of polynomials not vanishings inside a circle, Journal of Inequalities in Pure and Applied Mathematics, Volume: 6, Issue: 2, Articale: 53, ss:1-21.
11. Milonovic’ G.V., Mitrinovic’ D.S., and Rassias, M.TH., (1994). Extremal Problems, Inequalities Zeros (ord Scientific Publ. Co., Singapore, New Jersey, London.
12. Mir, A., Devan, K.K., and Sing, N., (2009). Some inequalities concerning the rate of growty of polinomials, Turk. J. Math., 33, ss:239-247.
13. 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, ss: 3-4.
14. Ostrowski, A.M., (1979). Notiz uber Maximalwerte von polynomen auf dem einheitskreis, Üniv. Beograd, publ.Elektrotehn. Fak.,ser. Mat. Fiz., No 34-637 ,ss: 55-56.
15. Quazi, M.A., (1992). On the maximum module values of polynomials, Proceding of the American Mathematicle Soc., Volume: 115, Number: 2, ss:337-343.
16. Rassias, M.T.H., (1986). A new inequality for complex-valued polynomial functions, Proc. Amer. Math. Soc. 9, ss: 296-298.