e-ISSN: 2636-8714 | Journal of Advanced Mathematics and Mathematics Education - JAMAME Sign In  |  Register
ZALCMAN CONJECTURE FOR SOME SUBCLASSES OF ANALYTIC FUNCTIONS DEFINED BY SALAGEAN OPERATOR
EVRİM TOKLU
Published Online : 18 February 2018
Article Views: 25 | Article Download: 25  Full PDF

Abstract

The aim of this investigation is to give a new subclass of analytic functions dened by Salagean dierential operator and nd upper bound of Zalcman functional a2 n
Keywords : Univalent function, bi-univalent function, Coecient bounds.

References

[1] D. Bansal and J. Sokol, Zalcman conjecture for some subclass of analytic functions, J. Fract. Calc. Appl., Vol. 8(1) Jan. 2017, pp. 1-5.

[2] J.E. Brown and A. Tsao, On the Zalcman conjecture for starlikeness and typically real functions, Math. Z., 191 (1986), 467474.

[3] P.L. Duren, Univalent Functions, Grundlehren der Mathematischen Wis- senschaften, Vol. 259. Springer:New York, NY,USA, 1983.

[4] A.E. Livingston, The coecients of multivalent close-to-convex functions, Proc. Amer. Math. Soc., 21 (1969), 545552.

[5] W. Ma, The Zalcman conjecture for close-to-convex functions, Proc. Amer. Math. Soc., 104(1988), 741744.

[6] J. Nishiwaki, S. Owa, Coecient inequalities for certain analytic functions, Int. J. Math. Math. Sci. 29(2002) 285290.

[7] M. Nunokawa,A sucient condition for univalence and starlikeness, Proc. Japan Acad. Ser. A., 65(1989) 163164.

[8] C. Pommerenke, Univalent Functions. Gottingen, Germany: Vandenhoeck and Rupercht, 1975.

[9] 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.

[10] G.S. Salagean, Subclasses of univalent functions, in Complex Analysis, Fifth Romanian-Finnish Seminar, Vol. 1013 of Lecture Notes in Mathematics, pp. 362- 372, Springer, Berlin, Germany, 1983.

[11] R. Singh, S. Singh, Some sucient conditions for univalence and starlikeness Collect. Math., 47(1982) 309314.

[12] B.A. Uralegaddi, M.D. Ganigi, S. M. Sarangi, Univalent functions with positive coecients Tamkang J. Math., 25(1994) 225230