Starlikeness of Double Integral operators
DOI:
https://doi.org/10.5644/SJM.10.1.06Keywords:
Starlike functions, differential subordination, integral operatorsAbstract
In this paper we investigate starlikeness of double integral operators by using second-order differential inequalities. We shall give some interesting conditions for $f(z)$ defined by double integral operators to be starlike of order $\beta$.
Downloads
References
R. Aghalary and A. Ebadian, New coefficient conditions for functions starlike with respect to symmetric points, Serdica Math. J., 36 (2010), 211--222.
R. M. Ali, S. K. Lee, K. G. Subramanian and A. Swaminathan, A third-order differential equation and starlikeness of a double integral operator, Abstr. Appl. Anal., (2011), Art. ID 901235, 10 pp.
D. J. Hallenbeck and St. Ruscheweyh, Subordination by convex functions, Proc. Amer. Math. Soc., 52 (1975), 191--195.
K. Kuroki and S. Owa, Double integral operators concerning starlike of order $beta$, Int. J. Differ. Equ., (2009) 1--13.
S. S. Miller and P. T. Mocanu, Double integral starlike operators, Integral Transforms Spec. Funct., 19 (7-8) (2008), 591--597.
M. Obradović, Simple sufficient conditions for univalence, Mat. Vesnik, 49 (1997), 241--244.
J. Sokól, On sufficient condition for starlikeness of certain integral of analytic function, J. Math, Appl., 26 (2006), 127--130.
J. Sokól, On a condition for $alpha$-starlikeness, J. Math. Anal. Appl., 352 (2009), 696--701.
