Ma-Minda starlikeness of certain analytic functions

Baskar Babujee Janani, V. Ravichandran

Abstract


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.

Keywords


Univalent functions; starlike functions; convex functions; subordination; radius of starlikeness.

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References


R. M. Ali, N. K. Jain and V. Ravichandran, Radii of starlikeness associated with the lemniscate of Bernoulli and the left-half plane, Appl. Math. Comput. 218 (2012), no. 11, 6557–6565.

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

P. L. Duren, Univalent functions, Grundlehren der mathematischen Wissenschaften, 259, Springer-Verlag, New York, 1983.

S. Gandhi and V. Ravichandran, Starlike functions associated with a lune, Asian-Eur. J. Math. 10 (2017), no. 4, 1750064, 12 pp.

A. Gangadharan, V. Ravichandran and T. N. Shanmugam, Radii of convexity and strong starlikeness for some classes of analytic functions, J. Math. Anal. Appl. 211 (1997), no. 1, 301–313.

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

W. Janowski, Some extremal problems for certain families of analytic functions. I, Ann. Polon. Math. 28 (1973), 297–326.

R. Kanaga and V. Ravichandran, Starlikeness for certain close-to-star functions, Hacet. J. Math. Stat. 50 (2021), no. 2, 414–432.

S. S. Kumar and K. Arora, Starlike Functions associated with a Petal Shaped Domain, arXiv: 2011.10072 (2020), 15 pages.

S. S. Kumar and G. Kamaljeet, A cardioid domain and starlike functions, Anal. Math. Phys. 11 (2021), no. 2, Paper No. 54, 34 pp.

A. Lecko, V. Ravichandran and A. Sebastian, Starlikeness of certain non-univalent functions, Anal. Math. Phys. 11 (2021), no. 4, Paper No. 163, 23 pp.

S. K. Lee, K. Khatter and V. Ravichandran, Radius of starlikeness for classes of analytic functions, Bull. Malays. Math. Sci. Soc. 43 (2020), no. 6, 4469–4493.

W. C. Ma and D. Minda, 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.

S. Madhumitha and V. Ravichandran, Radius of starlikeness of certain analytic functions, Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Mat. RACSAM 115 (2021), no. 4, Paper No. 184, 18 pp.

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

N. K. Jain and V. Ravichandran, Product and convolution of certain univalent functions, Honam Math. J. 38 (2016), no. 4, 701–724.

R. K. Raina and J. Sok´oł, Some properties related to a certain class of starlike functions, C. R. Math. Acad. Sci. Paris 353 (2015), no. 11, 973–978.

V. Ravichandran, F. Rønning and T. N. Shanmugam, Radius of convexity and radius of starlikeness for some classes of analytic functions, Complex Variables Theory Appl. 33 (1997), no. 1-4, 265–280.

A. Sebastian and V. Ravichandran, Radius of starlikeness of certain analytic functions, Math. Slovaca 71 (2021), no. 1, 83–104.

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

H. Silverman and E. M. Silvia, Subclasses of starlike functions subordinate to convex functions, Canad. J. Math. 37 (1985), no. 1, 48–61.

L. A. Wani and A. Swaminathan, Radius problems for functions associated with a nephroid domain, Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Mat. RACSAM 114 (2020), no. 4, Paper No. 178, 20 pp.

L. A. Wani and A. Swaminathan, Starlike and convex functions associated with a nephroid domain, Bull. Malays. Math. Sci. Soc. 44 (2021), no. 1, 79–104.




DOI: http://dx.doi.org/10.24193/subbmath.2025.1.02

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