AN APPLICATION OF CARATHEODORY FUNCTIONS

Let $\mathcal{P}(\alpha)$ be the class of functions $p(z)$ which are Carath\'eodory functions of order $\alpha \,(0 \leqq \alpha < 1)$ in the open unit disk $\mathbb{U}$. In view of the extremal function $L_0(\alpha;z)$ for the class $\mathcal{P}(\alpha)$, a new class $\mathcal{Q}(\beta)$ of functions $q(z)$ is introduced. The object of the present paper is to discuss some interesting coefficient inequalities for $q(z)$ in the class $\mathcal{Q}(\beta)$.

Keywords:

Analytic function, Carath\'eodory function, extremal function coefficient inequality,

PDF

___

[1] A. A. Attiya and M. A. Nasr, On sucient conditions for Caratheodory functions with applications , J. Inequ. Appl. 2013, No.191 (2013), 1 -10.
[2] C. Caratheodory, Uber den Variabilitatsbereich der Koeffzienten von Potenzreihen, die gegebene werte nicht annehmen, Math. Ann. 64(1907), 95-115.
[3] A. W. Goodman, Univalent Functions, Vol. I, Mariner Publ. Comp., Tampa, Florida, 1983
[4] I. H. Kim and N. E. Cho, Sufficient conditions for Caratheodory functions, Comp. Math. Appl. 59(2010), 2067- 2073.
[5] M. Nunokawa, S. Owa, N. Takahashi and H. Saitoh, Sufficient conditions for Caratheodory functions, Indian J. Pure Appl. Math. 33(2002), 1385-1390.
[6] N. Xu, Sufficient conditions and applications for Caratheodoty functions, J. Math. 2013, Article ID 930290 (2013), 1-4.

Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2013
Yayıncı: Mehmet Zeki SARIKAYA

Arşiv