ε-simultaneous approximation and invariant points

Invariant Points and ε-Simultaneous Approximation

Invariant Points of Best Approximation and Best Simultaneous Approximation

In this paper we generalize and extend BrosowskiMeinardus type results on invariant points from the set of best approximation to the set of best simultaneous approximation, which is not necessarily starshaped. As a consequence some results on best approximation are deduced. The proved results extend and generalize some of the results of R. N. Mukherjee and V. Verma [Publ. de l’Inst. Math. 49(19...

VC Dimension, ε-nets and ε-approximation

“I’ve never touched the hard stuff, only smoked grass a few times with the boys to be polite, and that’s all, though ten is the age when the big guys come around teaching you all sorts to things. But happiness doesn’t mean much to me, I still think life is better. Happiness is a mean son of a bitch and needs to be put in his place. Him and me aren’t on the same team, and I’m cutting him dead. I...

Common Fixed Points, Invariant Approximation and Generalized Weak Contractions

Width invariant approximation of fuzzy numbers

In this paper, we consider the width invariant trapezoidal and triangularapproximations of fuzzy numbers. The presented methods avoid the effortful computation of Karush-Kuhn-Tucker Theorem. Some properties of the new approximation methods are presented and the applicability of the methods is illustrated by examples. In addition, we show that the proposed approximations of fuzzy numbers preserv...