Radius problems for certain classes of analytic functions
DOI:
https://doi.org/10.24193/subbmath.2023.4.04Keywords:
Starlike function, radius of starlikeness, exponential functionAbstract
Radius constants for functions in three classes of analytic
functions to be a starlike function of order \(\alpha\), parabolic starlike func-
tion, starlike function associated with lemniscate of Bernoulli, exponen-
tial function, cardioid, sine function, lune, a particular rational function,
and reverse lemniscate are obtained. One of these classes are character-
ized by the condition \(Re g/(ze^z) > 0\). The other two classes are defined
by using the function g and they consist respectively of functions f
satisfying \(Ref/g>0\) and \(|f/g-1| < 1\).
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. Sivaprasad Kumar, and V. Ravichandran, Radius problems for starlike functions associated with the sine function, Bull. Iranian Math. Soc. 45 (2019), no. 1, 213-232.
A. S. A. El-Faqeer, M.H. Mohd, V. Ravichandran and S. Supramaniam, Star- likeness of certain analytic functions, preprint.
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.
R. Kanaga and V. Ravichandran, Starlikeness for certain close-to-star functions, Hacett. J. Math. Stat. appeared online (https://dergipark.org.tr/en/download/article-le/1003494)
S. Kumar and V. Ravichandran, A subclass of starlike functions associated with a rational function, Southeast Asian Bull. Math. 40 (2016), no. 2, 199-212.
A. Lecko, V. Ravichandran, and A. Sebastian, Starlikeness of certain non-univalent function, preprint.
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-
V. Madaan, A. Kumar, and V. Ravichandran, Radii of starlikeness and convexity of some entire functions, Bull. Malays. Math. Sci. Soc. 43(2020), no. 6 ,
-4359.
R. Mendiratta, S. Nagpal and V. Ravichandran, A subclass of starlike functions associated with left-half of the lemniscate of Bernoulli, Internat. J. Math. 25 (2014), no. 9, 1450090, 17 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.
R. K. Raina and J. Sokol, Some properties related to a certain class of starlike functions, C. R. Math. Acad. Sci. Paris 353 (2015), no. 11, 973-978.
F. Ronning, Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc. 118 (1993), no. 1, 189-196.
A. Sebastian and V. Ravichandran, Radius of starlikeness of certain analytic functions, Math. Slovaca, accepted.
G. M. Shah, On the univalence of some analytic functions, Pacic J. Math. 43 (1972), 239-250.
T. N. Shanmugam and V. Ravichandran, Certain properties of uniformly convex functions, in Computational methods and function theory 1994 (Penang),
-324, Ser. Approx. Decompos., 5, World Sci. Publ., River Edge, NJ.
K. Sharma, N. K. Jain and V. Ravichandran, Starlike functions associated with a cardioid, Afr. Mat. 27 (2016), no. 5-6, 923-939.
J. Sokol and J. Stankiewicz, Radius of convexity of some subclasses of strongly starlike functions, Zeszyty Nauk. Politech. Rzeszowskiej Mat. No. 19 (1996),
-105.
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