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A Fractal Example of a Continuous Monotone Function with Vanishing Derivatives on a Dense Set and Infinite Derivatives on Another Dense Set
Sierpinki Gasket harmonic function
2011/6/2
Inspired by the theory of analysis on fractals, we construct an example of a continuous, monotone function on an interval, which has vanishing derivatives on a dense set and infinite derivatives on an...
Convex Multivariate Approximation by Algebras of Continuous Functions
Convex Multivariate Approximation Algebras Continuous Functions
2010/11/22
We obtain an analog of Shvedov theorem for convex multivariate approximation by algebras of continuous functions.
Lipschitz Continuous Selectors, Part I：Linear Selectors
Linear Selectors Lipschitz Continuous Selectors
2009/1/23
We study various properties of Lipschitz continuous linear selectors on the family of all convex, nonempty and compact subsets of $\mathbb{R}^n$. In particular, it is shown that if $s$ is such a selec...
Characterizations of Generalized Monotone Nonsmooth Continuous Maps using Approximate Jacobians
Monotone maps quasimonotone maps pseudomonotone maps approximate Jacobians
2009/1/22
This paper presents necessary and/or sufficient conditions for a continuous map to be monotone, quasimonotone or pseudomonotone. The results are given in terms of approximate Jacobian matrices which r...
Existence of a Continuous Solution of Parametric Nonlinear Equation with Constraints
Continuous Solution Parametric Nonlinear Equation Constraints
2009/1/16
Combining a consequence of the Michael continuous selection theorem and an iterative scheme we prove the existence of a continuous solution of a parametric equation with constraints. An inverse functi...