Radii of Starlikeness and Convexity for Analytic Functions with Fixed Second Coefficient Satisfying Certain Coefficient Inequalities

• 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.;

Abstract
For functions $f(z) 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, 2017, 40, 2, 819 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. 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. 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}$, Math. Comput. Modelling, 48(3-4)(2008), 402-419. 15. W. C. Ma and D. Minda, Uniformly convex functions, Ann. Polon. Math., 57(2)(1992), 165-175. 16. S. Nagpal and V. Ravichandran, Applications of the theory of differential subordination for functions with fixed initial coefficient to univalent functions, Ann. Polon. Math., 105(3)(2012), 225-238. 17. S. Nagpal and V. Ravichandran, Fully starlike and fully convex harmonic mappings of order${\alpha}\$, Ann. Polon. Math., 108(1)(2013), 85-107.

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