ZALCMAN CONJECTURE FOR SOME SUBCLASSES OF ANALYTIC FUNCTIONS DEFINED BY S ˘ AL ˘ AGEAN OPERATOR
Öz
The aim of this investigation is to give a new subclass of analytic functionsdefined by S˘al˘agean differential operator and find upper bound of Zalcman functionala2− a2n−1for functions belonging to this subclass for n = 3.n
Anahtar Kelimeler
Kaynakça
- D. Bansal and J. Sok´ol, Zalcman conjecture for some subclass of analytic functions, J. Fract. Calc. Appl., Vol. 8(1) Jan. 2017, pp. 1-5.
- J.E. Brown and A. Tsao, On the Zalcman conjecture for starlikeness and typically real functions, Math. Z., 191 (1986), 467474.
- P.L. Duren, Univalent Functions, Grundlehren der Mathematischen Wis- senschaften, Vol. 259. Springer:New York, NY,USA, 1983.
- A.E. Livingston, The coefficients of multivalent close-to-convex functions, Proc. Amer. Math. Soc., 21 (1969), 545552.
- W. Ma, The Zalcman conjecture for close-to-convex functions, Proc. Amer. Math. Soc., 104(1988), 741744.
- J. Nishiwaki, S. Owa, Coefficient inequalities for certain analytic functions, Int. J. Math. Math. Sci. 29(2002) 285290.
- M. Nunokawa,A sufficient condition for univalence and starlikeness, Proc. Japan Acad. Ser. A., 65(1989) 163164.
- C. Pommerenke, Univalent Functions. Gottingen, Germany: Vandenhoeck and Rupercht, 1975.
- H. Saitoh, M. Nunokawa, S. Fukui, S. Owa, A remark on close-to-convex and starlike functions, Bull. Soc. Roy. Sci. Liege, 57(1988) 137141.
- G.S. S˘al˘agean, Subclasses of univalent functions, in Complex Analysis, Fifth Romanian-Finnish Seminar, Vol. 1013 of Lecture Notes in Mathematics, pp. 362- , Springer, Berlin, Germany, 1983.