Some Properties for Certain Subclasses of Analytic Functions Associated with $k-$Integral Operators

Abstract

In this paper, the k-integral operators for analytic functions dened in the open unit disc U = fz 2 C : jzj < 1g are introduced. Several new subclasses of analytic functions satisfying certain relations involving these operators are also introduced. Further, we establish the inclusion relation for these subclasses. Next, the integral preserving properties of a k-integral operator satised by these newly introduced subclasses are obtained. Some applications of the results are discussed. Concluding remarks are also given.

Keywords

• $k$-integral operators
• Starlike functions
• Convex functions
• Subordination
• Inclusion relations

Kaynakça

1. [1] K. Al-Shaqsi and M. Darus, On certain subclasses of analytic functions defined by a multiplier transformation with two parameters, Appl. Math. Sci 3(36) (2009), 1799-1810.
2. [2] S. D. Bernardi, Convex and starlike univalent functions, Trans. Am. Math. Soc. 135(1969), 429-446.
3. [3] N.E. Cho and K.I. Noor, Inclusion properties for certain classes of meromorphic functions associated with the Choi-Saigo- Srivastava operator, J. Math. Anal. Appl. 320(2) (2006), 779-786.
4. [4] J.H. Choi, M. Saigo and H.M. Srivastava, Some inclusion properties of a certain family of integral operators, J. Math. Anal. Appl. 276(1) (2002), 432-445.
5. [5] R. Diaz and E. Pariguan, On hypergeometric functions and Pochhammer k-symbol, Divulgaciones Matemtcas 15(2) (2007), 179-192.
6. [6] P. Eenigenburg, S. Miller, P. Mocanu and M. Reade, On a Briot-Bouquet differential subordination, Revue Roumaine de Math. Pures Appl. 29(7) (1984), 567-573.
7. [7] C.Y. Gao, S.-M. Yuan and H.M. Srivastava, Some functional inequalities and inclusion relationships associated with certain families of integral operators, Comput. Math. Appl. 49(11-12) (2005), 1787-1795.
8. [8] I.B. Jung, Y.C. Kim and H.M. Srivastava, The Hardy space of analytic functions associated with certain one-parameter families of integral operators, J. Math. Anal. Appl. 176(1) (1993), 138-147.

9. [9] W. Ma and D. Minda, A unified treatment of some special classes of univalent functions, Proceeding of the Conference on Complex Analysis, Z. Li, F. Ren, L. Yang and S. Zhang (Eds), Int. Press (1994), 157-169.
10. [10] S.S. Miller and P.T. Mocanu, Differential subordinations: theory and applications, CRC Press (2000).
11. [11] S.S. Miller and P.T. Mocanu , Differential subordinations and univalent functions., Mich. Math. J. 28(2) (1981), 157-172.
12. [12] G. Murugusundaramoorthy and N. Magesh, On certain subclasses of analytic functions associated with hypergeometric functions, Appl. Math. Lett. 24(4) (2011), 494-500.
13. [13] K.I. Noor, On quasi-convex functions and related topics, Int. J. Math. Math. Sci. 10(2) (1987), 241- 258.
14. [14] S. Porwal and K. K. Dixit, An application of generalized Bessel functions on certain analytic functions, Acta Univ. M. Belii Ser. Math. (2013), 51-57.
15. [15] E.D. Rainville, Special functions, Chelsea (1971).
16. [16] Z.G. Wang, C.Y. Gao and S.M. Yuan, On certain subclasses of close-to-convex and quasi-convex functions with respect to k-symmetric points, J. Math. Anal. Appl. 322(1) (2006), 97-106.