On a Subclass of Multivalent Functions with Bounded Positive Real Part
DOI:
https://doi.org/10.14419/ijams.v7i1.29129Keywords:
Multivalent Functions, - Symmetric Points, Differential Subordination.Abstract
In the present paper, by introducing a new subclass of multivalent functions with respect to - symmetric points, we have obtained the integral representations and conditions for starlikeness using differential subordination.
References
1. R. M. Ali, A. O. Badghaish and V. Ravichandran, "Multivalent functions with
respect to - ply points and symmetric conjugate points", Comput. Math. Appl., 60, no.~11, (2010), 2926--2935.
2. R. Chandrashekar, Rosihan M Ali, S. K. Lee, V. Ravichandran, "Convolutions of meromorphic multivalent functions with respect to -ply points and symmetric conjugate points", Appl. Math. Comput. 218, no. 3, (2011), 723--728.
3. K. Kuroki and S. Owa, "Notes on new class for certain analytic functions", RIMS Kokyuroku, 1772 (2011) pp. 21–25.
4. K. R. Karthikeyan, K. Srinivasan and K. Ramachandran, "On A Class Of Multivalent Starlike Functions With A Bounded Positive Real Part", Palestine Journal of Mathematics, Vol. 5(1) (2016) , 59--64.
5. P. Liczberski and J. Pol ubi'nski, "On -symmetrical functions", Math. Bohem., 120, no.~1, (1995), 13--28.
6. S. S. Miller and P. T. Mocanu, "Subordinants of differential superordinations", Complex Var. Theory Appl., 48, no. 10 (2003), 815--826.
7. R. Parvatham, S. Radha, "On -starlike and -close-to-convex functions with respect to symmetric points", Indian J. Pure Appl. Math., 17, no. 9 (1986), 1114--1122.
8. K. Sakaguchi, "On a certain univalent mapping", J. Math. Soc. Japan, 11 (1959), 72--75.
9. Z. G. Wang, C. Y. Gao and S. M. Yuan, "On certain subclasses of close-to-convex and quasi-convex functions with respect to -symmetric points", J. Math. Anal. Appl. , 322, no.~ 1, (2006), 97--106.
10. Z. G. Wang, Y.P. Jiang and H. M. Srivastava, "Some subclasses of multivalent analytic functions involving the Dziok-Srivastava operator", Integral Transforms Spec. Funct., 19, no.~1-2 (2008), 129--146.
11. N. Xu and D. Yang, "Some criteria for starlikeness and strongly starlikeness", Bull. Korean Math. Soc., 42, no. 3 (2005), 579--590.
12. S. M. Yuan and Z. M. Liu, "Some properties of -convex and -quasi convex functions with respect to -symmetric points", Appl. Math. Comput., 188, no.~2,(2007), 1142--1150.