LOEWNER CHAINS AND UNIVALENCE CRITERIA RELATED WITH RUSCHEWEYH AND S&#258;L&#258;GEAN DERIVATIVES

Erhan Deniz; Halit Orhan

doi:10.11948/2015036

2015 Volume 5 Issue 3

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Erhan Deniz, Halit Orhan. LOEWNER CHAINS AND UNIVALENCE CRITERIA RELATED WITH RUSCHEWEYH AND SĂLĂGEAN DERIVATIVES[J]. Journal of Applied Analysis & Computation, 2015, 5(3): 465-478. doi: 10.11948/2015036

Citation:

Erhan Deniz, Halit Orhan. LOEWNER CHAINS AND UNIVALENCE CRITERIA RELATED WITH RUSCHEWEYH AND SĂLĂGEAN DERIVATIVES[J]. Journal of Applied Analysis & Computation, 2015, 5(3): 465-478. doi: 10.11948/2015036

LOEWNER CHAINS AND UNIVALENCE CRITERIA RELATED WITH RUSCHEWEYH AND SĂLĂGEAN DERIVATIVES

Erhan Deniz¹,
Halit Orhan²

1 Department of Mathematics, Faculty of Science and Letters, Kafkas University, 36100 Kars, Turkey;
2 Department of Mathematics, Faculty of Science, Atatürk University, 25040 Erzurum, Turkey

Abstract

Abstract

In this paper we obtain, by the method of Loewner chains, some sufficient conditions for the analyticity and the univalence of the functions defined by an integral operator. These conditions involves Ruscheweyh and Sălăgean derivative operator in the open unit disk. In particular cases, we find the well-known conditions for univalency established by Becker[3], Ahlfors[2], Kanas and Srivastava[8] and others for analytic mappings f:U → C:Also, we obtain the corresponding new, useful and simpler conditions for this integral operator.
- Univalent function /
- Ruscheweyh and Sălăgean derivative /
- univalence condition /
- integral operator /
- Loewner chain
MSC: 30C45;30C55

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References

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