MATHEMATICA, 63 (86), N o 1, 2021, pp. 111–118 ON STARLIKENESS OF RECIPROCAL ORDER M.P. JEYARAMAN, V. AGNES SAGAYA JUDY LAVANYA, and H. AAISHA FARZANA Abstract. Sufficient conditions for functions defined in the unit disk to be star- like of reciprocal order are obtained. Also certain recent results are generalized. MSC 2010. 30C45, 30C80. Key words. Analytic functions, subordination, starlike function of reciprocal order. REFERENCES [1] M. Arif, M. Darus, M. Raza and Q. Khan, Coefficient bounds for some families of starlike and convex functions of reciprocal order, The Scientific World Journal, (2014), Article 989640, 6 pages. [2] B.A. Frasin and M.Ab. Sabri, Sufficient conditions for starlikeness of reciprocal order, Eur. J. Pure Appl. Math., 10 (2017), 871–876. [3] B.A. Frasin, Y. Talafha and T. Al-Hawary, Subordination results for classes of functions of reciprocal order, Tamsui Oxf. J. Inf. Math. Sci., 30 (2014), 81–89. [4] W. Janowski, Extremal problems for a family of functions with positive real part and for some related families, Ann. Polon. Math., 23 (1970/71), 159–177. [5] K. Khatter, V. Ravichandran and S. Sivaprasad Kumar, Starlike functions associated with exponential function and the lemniscate of Bernoulli, Rev. R. Acad. Cienc. Exactas F´ ıs. Nat. Ser. A Mat. RACSAM, 113 (2019), 233–253. [6] W.C. Ma and D. Minda, A unified treatment of some special classes of univalent func- tions In: Proceedings of the Conference on Complex Analysis (Tianjin, 1992), pp. 157– 169, Conf. Proc. Lecture Notes Anal., I, Int. Press, Cambridge, MA. [7] S.S. Miller and P.T. Mocanu, Second-order differential inequalities in the complex plane, J. Math. Anal. Appl., 65 (1978), 289–305. [8] S.S. Miller and P.T. Mocanu, Differential subordinations, Monographs and Textbooks in Pure and Applied Mathematics, 225, Marcel Dekker, Inc., New York, 2000. [9] M. Nunokawa, S.P. Goyal and R. Kumar, Sufficient conditions for starlikeness, J. Class. Anal., 1 (2012), 85–90. [10] M. Nunokawa, S. Owa, J. Nishiwaki, K. Kuroki and T. Hayami, Differential subordina- tion and argumental property, Comput. Math. Appl., 56 (2008), 2733–2736. [11] V. Ravichandran, C. Selvaraj and R. Rajalaksmi, Sufficient conditions for starlike func- tions of order α, JIPAM. J. Inequal. Pure Appl. Math., 3 (2002), Article 81, 6 pages. [12] V. Ravichandran and S. Sivaprasad Kumar, Argument estimate for starlike functions of reciprocal order, Southeast Asian Bull. Math., 35 (2011), 837–843. [13] M.S. Robertson, Certain classes of starlike functions, Michigan Math. J.,32 (1985), 135–140. The authors are thankful to the referees for their insightful suggestions. DOI: 10.24193/mathcluj.2021.1.10