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Radius of Close-to-convexity of Harmonic Functions
Coefficient inequality partial sums radius of univalence analytic univalent convex and starlike harmonic functions
2011/8/24
Abstract: Let ${\mathcal H}$ denote the class of all normalized complex-valued harmonic functions $f=h+\bar{g}$ in the unit disk ${\mathbb D}$, and let $K=H+\bar{G}$ denote the harmonic Koebe function...
A Note on Quasiconvexity and Rank-one Convexity for 2$\times$2 Matrices
Quasiconvexity 2$\times$2 Matrices Rank-one Convexity
2009/1/22
We report on an attempt to find a counterexample to the statement that rank-one convexity does not imply quasiconvexity in the case of 2$\times$2 matrices. The failure of such attempt is a consequence...
Total Convexity for Powers of the Norm in Uniformly Convex Banach Spaces
Uniformly Convex Banach Spaces Norm Total Convexity
2009/1/13
The aim of the paper is to show that, in uniformly convex Banach spaces, the powers of the norm with exponent r > 1 share a property called total convexity. Using this fact we establish a formula for ...
On Starlikeness and Convexity of Analytic Functions Satisfying a Differential Inequality
Multivalent function Starlike function Convex function Multiplier transformation
2010/1/22
In the present paper, the authors investigate a differential inequality defined by multiplier transformation in the open unit disk E = {z:|z|
ERROR BOUNDS FOR GLIMM DIFFERENCE APPROXIMATIONS FOR SCALAR CONSERVATION LAWS WITHOUT CONVEXITY
error bounds Glimm's scheme non-convexity
2007/12/12
In last century, D. Hoff and J. Smoller derived the error bounds for the Glimm difference approximations of the solutions to scalar conservation laws with convexity. Our work is to extend the correspo...