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 
@article{CRMATH_2016__354_1_7_0,
     author = {Mamoru Nunokawa and Janusz Sok\'o{\l}},
     title = {Some simple conditions for univalence},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {7--11},
     publisher = {Elsevier},
     volume = {354},
     number = {1},
     year = {2016},
     doi = {10.1016/j.crma.2015.10.001},
     language = {en},
}
TY  - JOUR
AU  - Mamoru Nunokawa
AU  - Janusz Sokół
TI  - Some simple conditions for univalence
JO  - Comptes Rendus. Mathématique
PY  - 2016
SP  - 7
EP  - 11
VL  - 354
IS  - 1
PB  - Elsevier
DO  - 10.1016/j.crma.2015.10.001
LA  - en
ID  - CRMATH_2016__354_1_7_0
ER  - 
%0 Journal Article
%A Mamoru Nunokawa
%A Janusz Sokół
%T Some simple conditions for univalence
%J Comptes Rendus. Mathématique
%D 2016
%P 7-11
%V 354
%N 1
%I Elsevier
%R 10.1016/j.crma.2015.10.001
%G en
%F CRMATH_2016__354_1_7_0
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

Cité par Sources :

Commentaires - Politique