Sufficient conditions for p-valence of regular functions

Noriyuki SONE

doi:10.2969/jmsj/01640406

Noriyuki SONE

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JOURNAL FREE ACCESS

1964 Volume 16 Issue 4 Pages 406-418

DOI https://doi.org/10.2969/jmsj/01640406

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Published: 1964 Received: May 04, 1964 Available on J-STAGE: September 26, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 26, 2006 Reason for correction: - Correction: TITLE Details: Wrong : Sufficient conditions for p-valence of regular functions
Right : Sufficient conditions for p-valence of regular functions

Date of correction: September 26, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) L. V. Ahlfors, Complex analysis, New York, 1953.
2) S. D. Bernardi, Convex, starlike, and level curves, Duke Math. J., 28 (1961), 57-72.
4) E. Hille, Analytic function theory, I, Boston, 1961/62.
5) W. Kaplan, Close-to-convex schlicht functions, Michigan Math. J., 1 (1952), 169-185.
6) S. Ogawa, Some criteria for univalence, J. Nara Gakugei Univ., 10 (1961), 7-12.
7) S. Ogawa, On some criteria for p-valence, J. Math. Soc. Japan, 13(1961), 431-441.
8) S. Ozaki, Some remarks on the univalency and multivalency of functions, Sci. Rep. Tokyo Bunrika Daigaku A, 2 (1934), 42-55.
9) G. Pólya und Szegö, Aufgaben und Lehrsätze aus der Analysis, I, Berlin, 1954.
10) M. O. Reade, On Umezawa's criteria for univalence II, J. Math. Soc. Japan, 10 (1958), 255-259.
11) M. S. Robertson, Analytic functions star-like in one direction, Amer. J. Math., 58 (1936), 465-472.
12) W. C. Royster, Convexity and starlikeness of analytic functions, Duke Math. J., 19 (1952), 447-457.
13) K. Sakaguchi, A note on p-valent functions, J. Math. Soc. Japan, 14 (1962), 312-321.
14) K. Sakaguchi, A representation theorem for a certain class of regular functions, J. Math. Soc. Japan, 15 (1963), 202-209.
15) N. Sone, A generalization of the concept 'convexity or starlikeness', Mem. Fac. Liberal Arts and Education Yamanashi Univ., 1962, 115-119.
16) N. Sone, Univalent functions and non-convex domains, J. Math. Soc. Japan, 15 (1963), 191-201.
17) Lad. Špacek, Contribution à la théorie des fonctions univalentes, Casopis Pest. Mat. Fys., 62 (1936), 12-19.
18) T. Umezawa, On the theory of univalent functions, Tohoku Math. J., 7 (1955), 212-228.

Right : [1] L. V. Ahlfors, Complex analysis, New York, 1953.
[2] S. D. Bernardi, Convex, starlike, and level curves, Duke Math. J., 28 (1961), 57-72.
[3] R. K. Brown, Univalent solutions of W"+pW=0, Canad. J. Math., 14 (1962), 69-78.
[4] E. Hille, Analytic function theory, I, Boston, 1961/62.
[5] W. Kaplan, Close-to-convex schlicht functions, Michigan Math. J., 1 (1952), 169-185.
[6] S. Ogawa, Some criteria for univalence, J. Nara Gakugei Univ., 10 (1961), 7-12.
[7] S. Ogawa, On some criteria for p-valence, J. Math. Soc. Japan, 13 (1961), 431-441.
[8] S. Ozaki, Some remarks on the univalency and multivalency of functions, Sci. Rep. Tokyo Bunrika Daigaku A, 2 (1934), 42-55.
[9] G. Pólya und Szegö, Aufgaben und Lehrsätze aus der Analysis, I, Berlin, 1954.
[10] M. O. Reade, On Umezawa's criteria for univalence II, J. Math. Soc. Japan, 10 (1958), 255-259.
[11] M. S. Robertson, Analytic functions star-like in one direction, Amer. J. Math., 58 (1936), 465-472.
[12] W. C. Royster, Convexity and starlikeness of analytic functions, Duke Math. J., 19 (1952), 447-457.
[13] K. Sakaguchi, A note on p-valent functions, J. Math. Soc. Japan, 14 (1962), 312-321.
[14] K. Sakaguchi, A representation theorem for a certain class of regular functions, J. Math. Soc. Japan, 15 (1963), 202-209.
[15] N. Sone, A generalization of the concept ‘convexity or starlikeness’, Mem. Fac. Liberal Arts and Education Yamanashi Univ., 1962, 115-119.
[16] N. Sone, Univalent functions and non-convex domains, J. Math. Soc. Japan, 15 (1963), 191-201.
[17] Lad. Špacek, Contribution à la théorie des fonctions univalentes, Casopis Pêst. Mat. Fys., 62 (1936), 12-19.
[18] T. Umezawa, On the theory of univalent functions, Tôhoku Math. J., 7 (1955), 212-228.

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