Comptes Rendus
no. 1
Mathematical analysis
Some simple conditions for univalence
[Quelques conditions simples pour l'univalence]

Présenté par : the Editorial Board

Mamoru Nunokawa1 ; Janusz Sokół2
1 University of Gunma, Hoshikuki-cho 798-8, Chuou-Ward, Chiba, 260-0808, Japan
2 Department of Mathematics, Rzeszów University of Technology, Al. Powstańców Warszawy 12, 35-959 Rzeszów, Poland
Comptes Rendus. Mathématique, Volume 354 (2016) no. 1, pp. 7-11.

Nous appliquons le lemme de Ozaki et Umezawa sur les fonctions convexes dans une direction, afin de trouver des conditions suffisantes pour l'univalence et la presque convexité.

We apply Ozaki–Umezawa's lemma on functions that are convex in one direction to find some sufficient conditions for univalence and closeness to convexity.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.10.001
Mots-clés : Analytic, Univalent, Convex, Starlike, Close-to-convex, Differential subordination

Mamoru Nunokawa 1 ; Janusz Sokół 2

1 University of Gunma, Hoshikuki-cho 798-8, Chuou-Ward, Chiba, 260-0808, Japan
2 Department of Mathematics, Rzeszów University of Technology, Al. Powstańców Warszawy 12, 35-959 Rzeszów, Poland 
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Mamoru Nunokawa; Janusz Sokół. Some simple conditions for univalence. Comptes Rendus. Mathématique, Volume 354 (2016) no. 1, pp. 7-11. doi : 10.1016/j.crma.2015.10.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.10.001/

[1] F.G. Avhadiev; L.A. Aksentev The subordination principle in sufficient conditions for univalence, Dokl. Akad. Nauk SSSR, Volume 2 (1973) no. 1, pp. 934-939 (11)

[2] S.N. Kudryashov On some criteria of schlichtness of analytic functions, Mat. Zametki, Volume 13 (1973), pp. 359-366 (in Russian)

[3] S.S. Miller; P.T. Mocanu Differential Subordinations, Theory and Applications, Series of Monographs and Textbooks in Pure and Applied Mathematics, vol. 225, Marcel Dekker Inc., New York / Basel, 2000

[4] M. Nunokawa; T. Yaguchi; K. Takano; G. Salagean On a generalisation of Avhadiev and Aksentev's theorem, RIMS Kokyuroku, Volume 1727 (2011), pp. 60-63

[5] S. Ogawa Some criteria for univalence, J. Nara Gakugei Univ., Volume 10 (1961) no. 1, pp. 7-12

[6] S. Ozaki On the theory of multivalent functions II, Sci. Rep. Tokyo Bunrika Daigaku, Sect. A (1941), pp. 45-87

[7] G.M. Shah On holomorphic functions convex in one direction, J. Indian Math. Soc., Volume 37 (1973), pp. 257-276

[8] T. Umezawa On the theory of univalent functions, Tohoku Math. J., Volume 7 (1955), pp. 212-228

  • Kapil Jaglan; Anbareeswaran Sairam Kaliraj Criteria for close-to-convexity, convex in one direction of planar harmonic mappings, The Journal of Analysis, Volume 32 (2024) no. 3, p. 1381 | DOI:10.1007/s41478-023-00688-y
  • Mamoru Nunokawa; Nak Eun Cho; Oh Sang Kwon; Janusz Sokół Some sufficient conditions for univalence and close-to-convexity, Journal of Applied Analysis, Volume 26 (2020) no. 1, p. 91 | DOI:10.1515/jaa-2020-2007
  • Mamoru Nunokawa; Oh Sang Kwon; Young Jae Sim; Ji Hyang Park; Nak Eun Cho Conditions for one direction convexity and starlikeness, Journal of Inequalities and Applications, Volume 2016 (2016) no. 1 | DOI:10.1186/s13660-016-1034-z

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