Ma-Minda starlikeness of certain analytic functions
DOI:
https://doi.org/10.24193/subbmath.2025.1.02Keywords:
Univalent functions, starlike functions, convex functions, subordination, radius of starlikenessAbstract
A normalized analytic function defined on the open unit disc D is called Ma-Minda starlike if zf ′(z)/f(z) is subordinate to the function φ. For a normalized convex function f defined on D and α > 0, we determine the radius of Ma-Minda starlikeness of the function g defined as g(z) = (zf ′(z)/f(z))α f(z) for certain choices of φ. In particular, we investigate the radius of Janowski starlikeness of the function g.
Mathematics Subject Classification (2010): 30C80, 30C45.
Received 31 July 2023; Accepted 31 October 2023.
References
[1] Ali, R.M., Jain, N.K., Ravichandran, V., Radii of starlikeness associated with the lemniscate of Bernoulli and the left-half plane, Appl. Math. Comput., 218(11)(2012), 6557– 6565.
[2] Arora, K., Sivaprasad Kumar, S., Starlike functions associated with a petal shaped domain, Bull. Korean Math. Soc., 59(4)(2022), 993–1010.
[3] 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(1)(2019), 213– 232.
[4] Duren, P.L., Univalent Functions, vol. 259 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag, New York, 1983.
[5] Gandhi, S., Ravichandran, V., Starlike functions associated with a lune, Asian-Eur. J. Math., 10(4)(2017), 1750064, 12.
[6] Gangadharan, A., Ravichandran, V., Shanmugam, T.N., Radii of convexity and strong starlikeness for some classes of analytic functions, J. Math. Anal. Appl., 211(1)(1997), 301–313.
[7] Goel, P., Sivaprasad Kumar, S., Certain class of starlike functions associated with modified sigmoid function, Bull. Malays. Math. Sci. Soc., 43(1)(2020), 957–991.
[8] Janowski, W., Some extremal problems for certain families of analytic functions, I, Ann. Polon. Math., 28(1973), 297–326.
[9] Kanaga, R., Ravichandran, V., Starlikeness for certain close-to-star functions, Hacet. J. Math. Stat., 50(2)(2021), 414–432.
[10] Lecko, A., Ravichandran, V., Sebastian, A., Starlikeness of certain non-univalent functions, Anal. Math. Phys., 11(4)(2021), Paper No. 163, 23.
[11] Lee, S.K., Khatter, K., Ravichandran, V., Radius of starlikeness for classes of analytic functions, Bull. Malays. Math. Sci. Soc., 43(6)(2020), 4469–4493.
[12] 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), Conf. Proc. Lecture Notes Anal., I, pages 157–169. Int. Press, Cambridge, MA, 1994.
[13] Madhumitha, S., Ravichandran, V., Radius of starlikeness of certain analytic functions, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM, 115(4)(2021), Paper No. 184, 18.
[14] Mendiratta, R., Nagpal, S., Ravichandran, V., On a subclass of strongly starlike functions associated with exponential function, Bull. Malays. Math. Sci. Soc., 38(1)(2015), 365– 386.
[15] Raina, R.K., Sokół, J., Some properties related to a certain class of starlike functions, C.R. Math. Acad. Sci. Paris, 353(11)(2015), 973–978.
[16] Ravichandran, V., Rønning, F., Shanmugam, T.N., Radius of convexity and radius of starlikeness for some classes of analytic functions, Complex Variables Theory Appl., 33(1-4)(1997), 265–280.
[17] Sebastian, A., Ravichandran, V., Radius of starlikeness of certain analytic functions, Math. Slovaca, 71(1)(2021), 83–104.
[18] Sharma, K., Jain, N.K., Ravichandran, V., Starlike functions associated with a cardioid, Afr. Mat., 27(5-6)(2016), 923–939.
[19] Silverman, H., Silvia, E.M., Subclasses of starlike functions subordinate to convex functions, Canad. J. Math., 37(1)(1985), 48–61.
[20] Sivaprasad Kumar, S., Kamaljeet, G., A cardioid domain and starlike functions, Anal. Math. Phys., 11(2)(2021), Paper No. 54, 34.
[21] Wani, L.A., Swaminathan, A., Radius problems for functions associated with a nephroid domain, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM, 114(4)(2020), Paper No. 178, 20.
[22] Wani, L.A., Swaminathan, A., Starlike and convex functions associated with a nephroid domain, Bull. Malays. Math. Sci. Soc., 44(1)(2021), 79–104.
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