On some first-order differential subordination
Nunokawa, M., Duman, E., Sokoł, J., Cho, N., Owae, S. (2013). On some first-order differential subordination. EKB Journal Management System, 22(2), 197-200.
M. Nunokawa; E. Yavuz Duman; J. Sokoł; N.E. Cho; S. Owae. "On some first-order differential subordination". EKB Journal Management System, 22, 2, 2013, 197-200.
Nunokawa, M., Duman, E., Sokoł, J., Cho, N., Owae, S. (2013). 'On some first-order differential subordination', EKB Journal Management System, 22(2), pp. 197-200.
Nunokawa, M., Duman, E., Sokoł, J., Cho, N., Owae, S. On some first-order differential subordination. EKB Journal Management System, 2013; 22(2): 197-200.

On some first-order differential subordination

Journal of the Egyptian Mathematical Society
Volume 22, Issue 2, October 2014, Pages 197-200    PDF (424.75 K)
Document Type: Original Article
Authors
M. Nunokawa1; E. Yavuz Duman2; J. Sokoł3; N.E. Cho4; S. Owae5
1University of Gunma, Hoshikuki-cho 798-8, Chuou-Ward, Chiba 260-0808, Japan
2Department of Mathematics and Computer Science, I_stanbul Ku¨ltu¨r University, I_stanbul, Turkey
3Department of Mathematics, Rzeszo´w University of Technology, Al. Powstan´co´w Warszawy 12, 35-959 Rzeszo´w, Poland
4Department of Applied Mathematics, College of Natural Sciences, Pukyong National University, Pusan 608-737, Republic of Korea
5e Department of Mathematics, Kinki University, Higashi-Osaka, Osaka 577-8502, Japan
Abstract
Let A denote the class of functions f that are analytic in the unit disc D and normalized
by f(0) = f 0(0)  1=0. In this paper, we investigate the class of functions such that
Reff 0ðzÞ þ zf 00ðzÞ  bg > a in D. We determine conditions for a and b under which the function
f is univalent, close-to-convex, and convex. To obtain this, we first estimate OEArg{f 0(z)}OE which
improves the earlier results.
Keywords
Close-to-convex functions; Convex functions; Starlike functions; Subordination
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