Comptes Rendus
no. 1
Complex analysis
Generalizations of starlike harmonic functions
[Généralisations des fonctions harmoniques étoilées]

Présenté par : the Editorial Board

Jacek Dziok1 ; Maslina Darus2 ; Janusz Sokół3 ; Teodor Bulboacă4
1 Faculty of Mathematics and Natural Sciences, University of Rzeszów, ul. Prof. Pigonia 1, 35-310 Rzeszów, Poland
2 Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor Darul Ehsan, Malaysia
3 Department of Mathematics, Rzeszów University of Technology, Al. Powstańców Warszawy 12, 35-959 Rzeszów, Poland
4 Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania
Comptes Rendus. Mathématique, Volume 354 (2016) no. 1, pp. 13-18.

Dans cette Note, nous étudions des généralisations des classes de fonctions harmoniques liées aux fonctions de Janowski. En utilisant la théorie des points extrémaux, nous obtenons des estimations de coefficients, des théorèmes de distorsion et des inégalités de moyenne intégrale dans ces classes de fonctions.

In this paper we investigate some generalizations of classes of harmonic functions. By using the extreme points theory we obtain coefficients estimates distortion theorems and integral mean inequalities in these classes of functions.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.08.001
Mots-clés : Harmonic functions, Ruscheweyh derivative, Subordination, Extreme points, Starlike functions

Jacek Dziok 1 ; Maslina Darus 2 ; Janusz Sokół 3 ; Teodor Bulboacă 4

1 Faculty of Mathematics and Natural Sciences, University of Rzeszów, ul. Prof. Pigonia 1, 35-310 Rzeszów, Poland
2 Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor Darul Ehsan, Malaysia
3 Department of Mathematics, Rzeszów University of Technology, Al. Powstańców Warszawy 12, 35-959 Rzeszów, Poland
4 Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania 
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Jacek Dziok; Maslina Darus; Janusz Sokół; Teodor Bulboacă. Generalizations of starlike harmonic functions. Comptes Rendus. Mathématique, Volume 354 (2016) no. 1, pp. 13-18. doi : 10.1016/j.crma.2015.08.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.08.001/

[1] G. Choquet Sur un type de transformation analytique généralisant la représentation conforme et définie au moyen de fonctions harmoniques, Bull. Sci. Math., Volume 89 (1945), pp. 156-165

[2] J. Clunie; T. Sheil Small Harmonic univalent functions, Ann. Acad. Sci. Fenn., Ser. A 1 Math., Volume 9 (1984), pp. 3-25

[3] J. Dziok On Janowski harmonic functions, J. Appl. Anal., Volume 21 (2015) no. 2

[4] J. Dziok Classes harmonic functions defined by subordination, Abstr. Appl. Anal. (2015)

[5] D.J. Hallenbeck; T.H. MacGregor Linear Problems and Convexity Techniques in Geometric Function Theory, Pitman Advanced Publishing Program, Pitman, Boston, 1984

[6] J.M. Jahangiri Coefficient bounds and univalence criteria for harmonic functions with negative coefficients, Ann. Univ. Mariae Curie-Skłodowska, Sect. A, Volume 52 (1998) no. 2, pp. 57-66

[7] J.M. Jahangiri Harmonic functions starlike in the unit disk, J. Math. Anal. Appl., Volume 235 (1999), pp. 470-477

[8] H. Kneser Losung der Aufgabe 41, Jahresber. Dtsch. Math.-Ver., Volume 36 (1926), pp. 123-124

[9] H. Lewy On the non-vanishing of the Jacobian in certain one-to-one mappings, Bull. Amer. Math. Soc., Volume 42 (1936), pp. 689-692

[10] P. Montel Sur les famillies de fonctions analytiques qui admettent des valeurs exceptionnelles dans un domaine, Ann. Sci. Éc. Norm. Supér., Volume 23 (1912), pp. 487-535

[11] T. Rado Aufgabe 41, Jahresber. Dtsch. Math.-Ver., Volume 35 (1926), p. 49

[12] S. Ruscheweyh New criteria for univalent functions, Proc. Amer. Math. Soc., Volume 49 (1975), pp. 109-115

[13] T. Sheil-Small Constants for planar harmonic mappings, J. Lond. Math. Soc., Volume 2 (1990), pp. 237-248

[14] H. Silverman Harmonic univalent functions with negative coefficients, J. Math. Anal. Appl., Volume 220 (1998), pp. 283-289

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