### Applications of first order differential subordination for functions with positive real part

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Ali, R. M., Cho, N. E., Ravichandran, V. and Kumar, S. S., Differential sub-ordination for functions associated with the lemniscate of Bernoulli, Taiwanese J. Math. 16 (2012), no. 3, 1017–1026.

Ali R. M., Ravichandran, V. and Seenivasagan, N. Sufficient conditions for

Janowski starlikeness, Int. J. Math. Math. Sci. 2007(2007), Art. ID 62925, 7pp.

Bulboac˘ a, T. Differential Subordinations and Superordinations. Recent Results, House of Scientific Book Publ., Cluj-Napoca, 2005.

Cho, N. E., Kumar, V., Kumar, S. S., Ravichandran, V. Radius problem for

sin-starlike functions, preprint.

Cho, N. E., Lee, H. J., Park, J. H. and Srivastava, R. Some applications of the first-order differential subordinations, Filomat 30 (2016) no. 6, 1465–1474.

Dorca, I. and Breaz, D. Subordination of certain subclass of convex function, Stud. Univ. Babe¸ s-Bolyai Math. 57 (2012), no. 2, 181–187.

Goluzin, G.M. On the majorization principle in function theory, Dokl. Akad. Nauk. SSSR, 42(1935), pp. 647–650.

Janowski, W. Extremal problems for a family of functions with positive real part and for some related families, Ann. Polon. Math. 23 (1970/1971), 159–177.

Kumar, S. S., Kumar, V., Ravichandran V., and Cho, N. E. Sufficient con-

ditions for starlike functions associated with the lemniscate of Bernoulli, J.

Inequal. Appl. 2013(2013), 176, 13 pp.

Kumar, S. and Ravichandran, V. A subclass of starlike functions associated with a rational function, Southeast Asian Bull. Math. 40 (2016) no. 2, 199–212.

Kumar, S. and Ravichandran, V. Subordinations for Functions with Positive Real Part, Complex Anal. Oper. Theory (2017), doi:10.1007/s11785-017-0690-4.

Ma, W. C. and Minda, D. A unified treatment of some special classes of univa-lent functions, in Proceedings of the Conference on Complex Analysis (Tianjin,1992), 157–169, Conf. Proc. Lecture Notes Anal., I, Int. Press, Cambridge, MA.

Mendiratta, R., Nagpal, S., and Ravichandran, V. On a subclass of strongly starlike functions associated with exponential function, Bull. Malays. Math. Sci. Soc. 38 (2015), no. 1, 365–386.

Miller, S. S. and Mocanu, P. T. On some classes of first-order differential

subordinations, Michigan Math. J. 32 (1985), no. 2, 185–195.

Miller, S.S. and Mocanu, P. T. Differential Subordinations: Theory and Appli-cations, Dekker, New York, 2000.

Nunokawa, M., Obradovi´ c M. and Owa, S. One criterion for univalency, Proc. Amer. Math. Soc. 106 (1989), no. 4, 1035–1037.

Omar, R. and Halim, S. A. Differential subordination properties of Sokó l-

Stankiewicz starlike functions, Kyungpook Math. J. 53 (2013), no. 3, 459–465.

Padmanabhan, K. S. and Parvatham, R. Some applications of differential

subordination, Bull. Austral. Math. Soc. 32 (1985), no. 3, 321–330.

Raina, R. K. and Sokó l, J. On coefficient estimates for a certain class of

starlike functions, Hacet. J. Math. Stat. 44 (2015), no. 6, 1427–1433.

Ravichandran, V. and Sharma, K. Sufficient conditions for starlikeness, J. Ko-rean Math. Soc. 52 (2015) no. 4, 727–749.

Shanmugam, T. N. Convolution and differential subordination, Internat. J.

Math. Math. Sci. 12 (1989), no. 2, 333–340.

Sharma, K., Jain, N. K. and Ravichandran, V. Starlike functions associated

with a cardioid, Afr. Mat. 27 (2016), no. 5-6, 923–939.

Sharma, K. and Ravichandran, V. Applications of subordination theory to

starlike functions, Bull. Iranian Math. Soc. 42 (2016) no. 3, 761–777.

Sok´ o l, J. and Stankiewicz, J. Radius of convexity of some subclasses of strongly starlike functions, Zeszyty Nauk. Politech. Rzeszowskiej Mat. No. 19 (1996), 101–105.

Tuneski, N., Bulboac˘ a, T., and Jolevska-Tunesk, B. Sharp results on linear combination of simple expressions of analytic functions, Hacet. J. Math. Stat. 45 (2016), no. 1, 121–128.

DOI: http://dx.doi.org/10.24193/subbmath.2018.3.02

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