Coefficient inequalities for starlikeness and convexity

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Published: Jun 21, 2012
DOI: https://doi.org/10.5556/j.tkjm.44.2013.1041
Keywords:
Convex function starlike function k-uniformly convex function coefficient inequality hypergeometric functions

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Ali Rosihan M.
School ofMathematical Sciences, Universiti SainsMalaysia, 11800 USM, Penang,Malaysia.
Mahnaz M. Nargesi
School ofMathematical Sciences, Universiti SainsMalaysia, 11800 USM, Penang,Malaysia.
Ravichandran V.
Department ofMathematics, University of Delhi, Delhi 110 007, India; School ofMathematical Sciences, Universiti SainsMalaysia, 11800 USM, Penang,Malaysia.

Abstract

For an analytic function $f(z)=z+\sum_{n=2}^\infty a_n z^n$ satisfying the inequality $\sum_{n=2}^\infty n(n-1)|a_n|\leq \beta$, sharp bound on $\beta$ is determined so that $f$ is either starlike or convex of order $\alpha$. Several other coefficient inequalities related to certain subclasses are also investigated.

Article Details

How to Cite
Rosihan M., A., M. Nargesi, M., & V., R. (2012). Coefficient inequalities for starlikeness and convexity. Tamkang Journal of Mathematics, 44(2), 149–162. https://doi.org/10.5556/j.tkjm.44.2013.1041
Issue
Vol. 44 No. 2 (2013)
Section
Papers
Author Biography

Ravichandran V., Department ofMathematics, University of Delhi, Delhi 110 007, India; School ofMathematical Sciences, Universiti SainsMalaysia, 11800 USM, Penang,Malaysia.

Visiting Professor, School of Mathematical Sciences, USM

References

O. P. Ahuja, Planar harmonic convolution operators generated by hypergeometric functions, Integral

Transforms Spec. Funct., 18(2007), 165--177.

R. M. Ali, Starlikeness associated with parabolic regions, Int. J. Math. Math. Sci., (2005), 561--570.

R. M. Ali, V. Ravichandran, Uniformly convex and uniformly starlike functions, Math. Newsletter, Ramanujan Math. Soc., 21(2011), 16--30.

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

Y. C. Kim and S. Ponnusamy, Sufficiency for Gaussian hypergeometric functions to be uniformly convex, Int. J. Math. Math. Sci., 22(1999), 765--773.

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

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(2008), 402--419.

S. Kanas and A. Wisniowska, Conic regions and $k$-uniform convexity, J. Comput. Appl. Math., 105(1999), 327--336.

E. P. Merkes, M. S. Robertson and W. T. Scott, On products of starlike functions, Proc. Amer. Math. Soc., 13(1962), 960--964.

S. Ponnusamy and F. Ronning, Starlikeness properties for convolutions involving hypergeometric series, Ann. Univ. Mariae Curie-Sklodowska Sect. A, 52(1998), 141--155.

H. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc., 51(1975), 109--116.

H. Silverman, Starlike and convexity properties for hypergeometric functions, J. Math. Anal. Appl., 172(1993), 574--581.

V. Singh, On some problems of Mocanu type, Indian J. Pure Appl. Math., 32 (2001), 1859--1867.

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