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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.

On the asymptotic partition of energy in the theory of swelling porous elastic soils

Gales C.

Archives of Mechanics

2003

Vol. 55, nr 1

91-107

The Cesaro means of various parts of the total energy are introduced in the context of the linear theory of swelling porous elastic soils. Then, the relations describing the asymptotic behavior of the Cesaro means are established.