Certain Classes of Analytic Functions Associated with Conic Domains

Year 2018, Issue: 24, 20 - 34, 14.08.2018

Nasir Khan

Abstract

In this paper, we define new subclasses of k-uniformly Janowski starlike and k-uniformly
Janowski convex functions associated with m-symmetric points. The integral representations, convolution
properties and sufficient conditions for the functions belong to this class are investigated.

Keywords

Subordination, convolution, m-symmetric points

References

• [1] R. Chand and P. Singh, On certain schlicht mapping, Ind. J. Pure App. Math. 10 (1979), 1167-1174.
• [2] W. Janowski, Some external problem for certain families of analytic functions I, Ann. Polon. Math., 28 (1973), 298-326.
• [3] S. Kanas and A. Wisniowska, Conic regions and k-uniform convexity, J. Comput. Appl. Math. 105(1999), 327-336.
• [4] S. Kanas and A. Wisniowska, Conic domains and starlike functions, Rev. Roumaine Math. Pure. Appl. 45 (2000), 647-657.
• [5] K. I. Noor and S. N. Malik, On coefficient inequalities of functions associated with conic domains, Comput. Math. Appl. 62 (2011), 2209-2217.
• [6] K. Sakaguchi, On a certain univalent mapping, J. Math. Soc. Japan. 11 (1959), 72- 75.
• [7] M. Arif, K. I. Noor and R. Khan, On subclasses of analytic functions with respect to symmetrical points, Abst. Appl. Anal. (2012), ID 790689, 11 pages.
• [8] K. I. Noor and S. Mustafa, Some classes of analytic functions related with functions of bounded radius rotation with respect to symmetrical points, J. Math. Ineq. 3 (2) (2009), 267-276.
• [9] T. N. Shanmugam, C. Ramachandran, and V. Ravichandran, Fekete-Szego problem for subclass of starlike functions with respect to symmetric points, Bull. Korean Math. Soc. 43 (3) (2006), 589-598.
• [10] O. Kwon and Y. Sim, A certain subclass of Janowski type functions associated with k-symmetric points, Commun. Korean Math. Soc. 28 (2013), 143-154.
• [11] S. Shams, S. R. Kulkarni, and J. M. Jahangiri, Classes of uniformly starlike and convex functions, Int. J. Math. Math. Sci. 55 (2004), 2959–2961.
• [12] H. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc. 51 (1975), 109–116.
• [13] S. S. Miller and P. T Mocanu, Subordinates of differential superordinations, Complex Variables, 48 (10) (2003), 815–826.
• [14] T. Bulboac a, Differential Subordinations and Superordinations, Recent Results, House of Scientic Book Publ, Cluj-Napoca, 2005.
• [15] A. Aral and V. Gupta, On q-Baskakov type operators, Demonstratio Math., 42 (1) (2009), 109–122.
• [16] R. N. Das and P. Singh, On subclasses of Schlicht mappings. Ind. J. Pure. App. Math. 8(1977), 864-872.