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Close-to-convexity properties of basic hypergeometric functions using their Taylor coefficients

Raghavendar K., Swaminathan A.

Journal of Mathematics and Applications

2012

Vol. 35

53--67

In this paper, we find the conditions on parameters a, b, c and q such that the basic hypergeometric function zφ(a,b;c;q,z) and its q-Alexander transform are close-to-convex (and hence univalent) in the unit disc D:={z: |z|<1}.

Coefficient conditions for univalency and starlikeness of analytic functions

Mondal S. R., Swaminathan A.

Journal of Mathematics and Applications

2009

Vol. 31

77-90

In this paper, we find conditions on the coefficients {a(k)} such that the corresponding analytic function f(z) and its partial sum fn(z) are close-to-convex with respect to some starlike function in the unit disc D. We also find conditions on these coefficients so that the analytic function is starlike univalent in D. As an application, we find conditions on the triplet (a, b, c) so that, the normalized Gaussian hypergeometric function and its particular cases, are in one of these classes.