Differential subordination for Janowski functions with positive real part

Swati Anand, Sushil Kumar, V Ravichandran

Abstract


Theory of differential subordination provides techniques to reduce differential subordination problems into verifying some simple algebraic condition called  admissibility condition. We exploit the first order  differential subordination theory to get several sufficient conditions for function satisfying several differential subordinations  to be a Janowski   function with positive real part.   As  applications, we obtain sufficient conditions for normalized analytic  functions to be Janowski starlike functions.

Keywords


Subordination; univalent functions; Carath\'eodory functions; starlike functions; Janowski function; admissible function

Full Text:

PDF

References


Ahuja, O. P., Kumar, S., and Ravichandran, V., Applications of first order differential subordination for functions with positive real part, Stud. Univ. Babe¸ s-Bolyai Math, 63(2018), no. 3, 303–311.

Ali, R. M., Ravichandran, V. and Seenivasagan, N., On Bernardi’s integral operator and the Briot-Bouquet differential subordination, J. Math. Anal. Appl. 324(2006) 663-668.

Ali, R. M., Ravichandran, V. and Seenivasagan, N., Sufficient conditions for Janowski starlikeness, Int. J. Math. Math. Sci. 2007, Art. ID 62925, 7 pp.

Anand, S., Kumar, S. and Ravichandran, V., Starlikeness associated with admissible functions, preprint.

Bohra, N., Kumar, S. and Ravichandran, V., Some Special Differential Subordinations, Hacet. J. Math. Stat.(2018), accepted.

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

Cho, N. E., Kumar, S., Kumar, V. and Ravichandran, V., Differential subordination and radius estimates for starlike functions associated with the Booth lemniscate, Turkish J. Math. 42 (2018), no. 3, 1380–1399.

Cho, N. E., Kumar, S., Kumar, V., Ravichandran, V. and Srivastava, H. M., Starlike Functions Related to the Bell Numbers, Symmetry, 11 (2019), no. 2, Article 219, 17 pp.

Chojnacka, O. and Lecko, A., Differential subordination of a harmonic mean to a linear function, Rocky Mountain J. Math. 48 (2018), no. 5, 1475–1484.

Gandhi, S., Kumar, S. and Ravichandran, V., First Order Differential Subordi nations for Caratheodory Functions, Kyungpook Math. J. 58 (2018), 257–270.

Goodman, A. W., Univalent functions. Vol. II, Mariner Publishing Co., Inc., Tampa, FL, 1983.

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.

Kanas, S., Techniques of the differential subordination for domains bounded by conic sections, Int. J. Math. Math. Sci. 2003, no. 38, 2389–2400.

Kanas, S., Differential subordination related to conic sections, J. Math. Anal. Appl. 317 (2006), no. 2, 650–658.

Kanas, S. and Lecko, A., Differential subordination for domains bounded by hyperbolas, Zeszyty Nauk. Politech. Rzeszowskiej Mat. 175 (1999), no. 23, 6170.

Kim, I. H., Sim,Y. J. and Cho,N. E., New criteria for Carath´ eodory functions, J. Inequal. Appl. 2019, 2019:13.

Kumar, S. and Ravichandran, V., Subordinations for Functions with Positive Real Part, Complex Anal. Oper. Theory 12 (2018), no. 5, 1179–1191.

Kumar, S. S., Kumar, V., Ravichandran, V. and Cho, N. E., Sufficient conditions for starlike functions associated with the lemniscate of Bernoulli, J. Inequal. Appl. 2013(2013), 176, 13 pp.

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, Monographs and Textbooks in Pure and Applied Mathematics, 225, Marcel Dekker, Inc., 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.

Sharma, K. and Ravichandran, V., Applications of subordination theory to starlike functions, Bull. Iranian Math. Soc. 42 (2016), no. 3, 761–777.

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

Robertson, M. S., Certain classes of starlike functions, Michigan Math. J. 32 (1985), no. 2, 135–140.

Seoudy, T. M. and Aouf, M. K., Classes of admissible functions associated with certain integral operators applied to meromorphic functions, Bull. Iranian Math. Soc. 41 (2015), no. 4, 793–804.

Tuneski, N. and Bulboac˘ a, T., Sufficient conditions for bounded turning of analytic functions, Ukra¨ın. Mat. Zh. 70 (2018), no. 8, 1118–1127.




DOI: http://dx.doi.org/10.24193/subbmath.2021.3.04

Refbacks

  • There are currently no refbacks.