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On Some Sufficient Conditions for a Function to Be p-Valent Starlike

1
Department of Mathematics, University of Gunma, Hoshikuki-cho 798-8, Chuou-Ward, Chiba 260-0808, Japan
2
College of Natural Sciences, University of Rzeszów, ul. Prof. Pigonia 1, 35-310 Rzeszów, Poland
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(11), 1417; https://doi.org/10.3390/sym11111417
Received: 21 October 2019 / Revised: 7 November 2019 / Accepted: 10 November 2019 / Published: 15 November 2019
A function f analytic in a domain D C is called p-valent in D, if for every complex number w, the equation f ( z ) = w has at most p roots in D, so that there exists a complex number w 0 such that the equation f ( z ) = w 0 has exactly p roots in D. The aim of this paper is to establish some sufficient conditions for a function analytic in the unit disc D to be p-valent starlike in D or to be at most p-valent in D . Our results are proved mainly by applying Nunokawa’s lemmas. View Full-Text
Keywords: univalent functions; starlike; convex; close-to-conve univalent functions; starlike; convex; close-to-conve
MDPI and ACS Style

Nunokawa, M.; Sokół, J.; Trybucka, E. On Some Sufficient Conditions for a Function to Be p-Valent Starlike. Symmetry 2019, 11, 1417.

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