Some negative theorems of approximation theory.

Negative Theorems in Approximation Theory

1. INTRODUCTION. Negative theorems have a rich tradition in mathematics. In fact mathematics seems to be unique among the sciences in that negative results are very much a part of the mathematical edifice. Most mathematical theories try to explain what is possible and also what is not. To understand the structure of a mathematical theory is also to understand its limitations. There are many dif...

Negative Theorems on Monotone Approximation

Approximation theorems on some classes of automata

This paper considers a machine as a pair (G5M) where G is a group or a semi group and where M is a state space. The first part of the paper called reversible-state machines considers the case where G is a locally compact group and M is any locally compact group and M is any locally compact space. The essential requirement is that (x,p)~>x(p) be continuous where XGG, peM and x(p)eM; i.e., we req...

Some approximation theorems via � - convergence Mustafa

The concept of -convergence was introduced in [P. Schaefer, Proc. Amer. Math. Soc. 36(1972)104-110] by using invariant mean.In this paper we apply this method to prove some Korovkin type approximation theorems. [Mustafa Obaid. Some approximation theorems via -convergence. Life Sci J 2012;9(4):1527-1530] (ISSN:10978135). http://www.lifesciencesite.com. 231

Some Theorems and Applications of Ramsey Theory

We present here certain theorems in Ramsey theory and some of their applications. First is Ramsey’s Theorem, which concerns the existence of monochromatic complete subgraphs of colored graphs that are large enough. One application is Schur’s Theorem, which is used for a result relating to Fermat’s Last Theorem. We then present the Hales-Jewett Theorem, which can be used to prove van der Waerden...