LINEAR COMBINATIONS OF q-STARLIKE FUNCTIONS OF ORDER ALPHA

Abstract

In this paper, we introduced a new concept of bounded radius rotation to dene the class of q-starlike functions of order  using the q-derivative, some geometric properties of linear combination of such functions are studied.

Keywords

• q-derivative,q-starlike functions,convex functions,linear combination,bounded radius rotation.

References

1. Agrawal, S. and Sahoo, S. K., (2014). Geometric properties of basic hypergeometric functions, Difference Equ. Appl., 20(11), pp. 1502-1522.
2. Agrawal, S. and Sahoo, S. K., (2017). A generalization of starlike functions of order alpha, Hokkaido Math. J., 46(1), pp. 15-27.
3. Goodman, A. W., (1983). Univalent Functions, Vol I. Washington, New Jersey: Polygonal Publishing House.
4. Ismail, M. E. H., Merkes, E., Styer, D. (1990). A generalization of starlike functions, Complex Variables, 14, pp. 77-84.
5. Jackson, F. H., (1909). On q-functions and a certain difference operator, Trans. Royal Soc. Edinburgh, 46, pp. 253-281.
6. Noor, K. I. and Noor, M. A., (2017). Linear combinations of generalized q-starlike functions, Appl. Math. Infor. Sci., 11(3), pp. 745-748.
7. Noor, K. I., and Riaz, S., (2017). Generalized q-starlike functions, Studia Scientiarum Mathematicarum Hungarica, 54(4) , pp. 509-522.
8. Raghavendar, K. and Swaminathan, A., (2012). Close-to-convexity of basic hypergeometric functions using their Taylor coefficients, J. Math. Appl., 35 , pp. 111-125.

9. Robertson, M. I., (1936). On the theory of univalent functions, Annals Math., pp. 374-408.
10. Sahoo, S. K. and Sharma, N. L., (2015). On a generalization of close-to-convex functions, Ann. Polon.Math., 113(1), pp. 93-108.