Differential subordination implications for certain Carathéodory functions

Authors

  • Meghna SHARMA Department of Mathematics, University of Delhi, India. Email: meghnasharma203@gmail.com. https://orcid.org/0000-0001-7446-4287
  • Sushil KUMAR Bharati Vidyapeeth’s College of Engineering, Delhi, India. Email: sushilkumar16n@gmail.com.
  • Naveen Kumar JAIN Department of Mathematics, Aryabhatta College, Delhi, India. Email: naveenjain05@gmail.com. https://orcid.org/0000-0003-0184-9965

DOI:

https://doi.org/10.24193/subbmath.2023.4.07

Keywords:

Differential subordination, Carathéodory function, starlike functions, sufficient conditions

Abstract

In this article, we wish to establish some first order differential subordination relations for certain Carathéodory functions with nice geometrical properties. Moreover, several implications are determined so that the normalized analytic function belongs to various subclasses of starlike functions

Mathematics Subject Classification (2010): 30C45.

Received 14 March 2021; Accepted 16 April 2021. Published Online: 2023-12-11 Published Print: 2023-12-30

References

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

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

Bohra, N., Kumar, S., Ravichandran, V., Some special differential subordinations, Hacet.

J. Math. Stat., 48(2019), no. 4, 1017-1034.

Cho, N.E., Kumar, V., Kumar, S.S., Ravichandran, V., Radius problems for starlike functions associated with the sine function, Bull. Iranian Math. Soc., 45(2019), no. 1, 213-232.

Cho, N.E., Kumar, S., Kumar, V., Ravichandran, V., Srivastava, H.M., Starlike functions related to the Bell numbers, Symmetry, 11(2019), Article ID 219, 1-17.

Ebadian, A., Mohammed, N.H., Adegani, E.A., Bulboacă, T., New results for some generalizations of starlike and convex functions, J. Funct. Spaces, 2020, Art. ID 7428648, 12 pp.

Gandhi, S., Kumar, S., Ravichandran, V., First order differential subordinations for Carathéodory functions, Kyungpook Math. J., 58(2018), no. 2, 257-270.

Goel, P., Kumar, S.S., Certain class of starlike functions associated with modified sigmoid function, Bull. Malays. Math. Sci. Soc., 43(2020), no. 1, 957-991.

Janowski, W., Extremal problems for a family of functions with positive real part and for some related families, Ann. Polon. Math., 23(1970/71), 159-177.

Kanas, S., Differential subordination related to conic sections, J. Math. Anal. Appl.,

(2006), no. 2, 650-658.

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

Kumar, S., Ravichandran, V., Subordinations for functions with positive real part, Complex Anal. Oper. Theory, 12(2018), no. 5, 1179-1191.

Ma, W.C., Minda, D., A unified treatment of some special classes of univalent 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., 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., Mocanu, P.T., On some classes of first-order differential subordinations, Michigan Math. J., 32(1985), no. 2, 185-195.

Miller, S.S., Mocanu, P.T., Differential Subordinations, Monographs and Textbooks in Pure and Applied Mathematics, 225, Marcel Dekker, Inc., New York, 2000.

Nunokawa, M., Obradović, M., Owa, S., One criterion for univalency, Proc. Amer. Math. Soc., 106(1989), no. 4, 1035-1037.

Nunokawa, M., Owa, S., Saitoh, S., Ahuja, O.P., On the quotient of the analytic representations of convex and starlike functions, Research Institute of Mathematical Analysis, 1112(1999), 63-69.

Raina, R.K., Sokół, J., On coefficient estimates for a certain class of starlike functions, Hacet. J. Math. Stat., 44(2015), no. 6, 1427-1433.

Sharma, K., Jain, N.K., Ravichandran, V., Starlike functions associated with a cardioid, Afr. Mat., 27(2016), no. 5-6, 923-939.

Silverman, H., Convex and starlike criteria, Int. J. Math. Math. Sci., 22(1999), no. 1, 75-79.

Yunus, Y., Halim, S.A., Akbarally, A.B., Subclass of starlike functions associated with a limacon, AIP Conf. Proc., 1(1974), 030023 (2018).

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Published

2023-12-11

How to Cite

SHARMA, M., KUMAR, S., & JAIN, N. K. (2023). Differential subordination implications for certain Carathéodory functions. Studia Universitatis Babeș-Bolyai Mathematica, 68(4), 775–787. https://doi.org/10.24193/subbmath.2023.4.07

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