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Radii of Starlikeness and Convexity for Analytic Functions with Fixed Second Coefficient Satisfying Certain Coefficient Inequalities
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  • Journal title : Kyungpook mathematical journal
  • Volume 55, Issue 2,  2015, pp.395-410
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2015.55.2.395
 Title & Authors
Radii of Starlikeness and Convexity for Analytic Functions with Fixed Second Coefficient Satisfying Certain Coefficient Inequalities
MENDIRATTA, RAJNI; NAGPAL, SUMIT; RAVICHANDRAN, V.;
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 Abstract
For functions with , , sharp radii of starlikeness of order <, convexity of order <, parabolic starlikeness and uniform convexity are derived when or (M>0). Radii constants in other instances are also obtained.
 Keywords
starlike functions;convex functions;uniformly convex functions;parabolic starlike functions;radius problems;fied second coefficient;
 Language
English
 Cited by
1.
Radius Problems for Ratios of Janowski Starlike Functions with Their Derivatives, Bulletin of the Malaysian Mathematical Sciences Society, 2016  crossref(new windwow)
 References
1.
R. M. Ali and V. Ravichandran, Uniformly convex and uniformly starlike functions, Math. Newsletter, 21(1)(2011), 16-30.

2.
R. M. Ali, S. Nagpal and V. Ravichandran, Second-order differential subordination for analytic functions with fixed initial coefficient, Bull. Malays. Math. Sci. Soc., 34(2011), 611-629.

3.
R. M. Ali, N. E. Cho, N. Jain and V. Ravichandran, Radii of starlikeness and convexity of functions defined by subordination with fixed second coefficients, Filomat, 26(3)(2012), 553-561. crossref(new window)

4.
R. M. Ali, M. M. Nargesi and V. Ravichandran, Radius constant for analytic functions with fixed second coefficient, The Scientific World Journal, 2014(2014), Article ID 898614, 6 pages.

5.
P. N. Chichra, New subclasses of the class of close-to-convex functions, Proc. Amer. Math. Soc., 62(1)(1976), 37-43.

6.
V. I. Gavrilov, Remarks on the radius of univalence of holomorphic functions, Mat. Zametki, 7(1970), 295-298.

7.
R. M. Goel and N. S. Sohi, Multivalent functions with negative coefficients, Indian J. Pure Appl. Math., 12(7)(1981), 844-853.

8.
A. W. Goodman, On uniformly convex functions, Ann. Polon. Math., 56(1)(1991), 87-92.

9.
W. Janowski, Some extremal problems for certain families of analytic functions. I, Ann. Polon. Math., 28(1973), 297-326.

10.
L. S. Keong, V. Ravichandran, S. Supramaniam, Applications of differential subordination for functions with fixed second coefficient to geometric function theory, Tamsui Oxford J. Inform. Math. Sci., 29(2)(2013), 267-284.

11.
Z. Lewandowski, S. Miller and E. Zlotkiewicz, Generating functions for some classes of univalent functions, Proc. Amer. Math. Soc., 56(1976), 111-117. crossref(new window)

12.
J.-L. Li and S. Owa, Sufficient conditions for starlikeness, Indian J. Pure Appl. Math., 33(3)(2002), 313-318.

13.
Z. W. Liu and M. S. Liu, Properties and characteristics of certain subclass of analytic functions, J. South China Normal Univ. Natur. Sci. Ed., 2010(3), 11-14.

14.
M.-S. Liu, Y.-C. Zhu and H. M. Srivastava, Properties and characteristics of certain subclasses of starlike functions of order ${\beta}$, Math. Comput. Modelling, 48(3-4)(2008), 402-419. crossref(new window)

15.
W. C. Ma and D. Minda, Uniformly convex functions, Ann. Polon. Math., 57(2)(1992), 165-175.

16.
S. Nagpal and V. Ravichandran, Applications of the theory of differential subordination for functions with fixed initial coefficient to univalent functions, Ann. Polon. Math., 105(3)(2012), 225-238. crossref(new window)

17.
S. Nagpal and V. Ravichandran, Fully starlike and fully convex harmonic mappings of order ${\alpha}$, Ann. Polon. Math., 108(1)(2013), 85-107. crossref(new window)

18.
K. S. Padmanabhan, On sufficient conditions for starlikeness, Indian J. Pure Appl. Math., 32(4)(2001), 543-550.

19.
C. Ramesha, S. Kumar and K. S. Padmanabhan, A sufficient condition for starlikeness, Chinese J. Math., 23(2)(1995), 167-171.

20.
V. Ravichandran, Radii of starlikeness and convexity of analytic functions satisfying certain coefficient inequalities, Math. Slovaca, 64(1)(2014), 27-38.

21.
M. O. Reade, On close-to-close univalent functions, Michigan Math. J., 3(1955), 59-62. crossref(new window)

22.
M. I. S. Robertson, On the theory of univalent functions, Ann. of Math., (2)37(2)(1936), 374-408.

23.
F. Ronning, Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc., 118(1)(1993), 189-196. crossref(new window)

24.
Y. Sun, Z.-G. Wang and R. Xiao, Neighbourhoods and partial sums of certain subclass of analytic functions, Acta Univ. Apulensis Math. Inform., No. 26(2011), 217-224.

25.
S. Yamashita, Radii of univalence, starlikeness, and convexity, Bull. Austral. Math. Soc., 25(3)(1982), 453-457. crossref(new window)