BİR FUL HİPERBOLİK BÖLGEDE EŞİTSİZLİKLER

Yıl 2014, Cilt: 9 Sayı: 1, 1 - 12, 01.02.2014

Adem Çelik

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

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