Differential subordination for Janowski functions with positive real part
DOI:
https://doi.org/10.24193/subbmath.2021.3.04Keywords:
Subordination, univalent functions, Carath\'eodory functions, starlike functions, Janowski function, admissible functionAbstract
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.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.
Downloads
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Transfer of copyright agreement: When the article is accepted for publication, the authors and the representative of the coauthors, hereby agree to transfer to Studia Universitatis Babeș-Bolyai Mathematica all rights, including those pertaining to electronic forms and transmissions, under existing copyright laws, except for the following, which the authors specifically retain: the authors can use the material however they want as long as it fits the NC ND terms of the license. The authors have all rights for reuse according to the license.
