Approximation in Real Contra-Continuous Functions Spaces

Abstract

Materials and Methods:

 In this paper I will study an approximation in real contra-continuous functions space starting from providing a best approximation element of this kind of functions in a compact set and I symbol of this space by   where  is real numbers .

Results:

Also in this paper I described contra-continuous function (as continuous functions) in real numbers also, I was able to get an example of this kind of functions in  (where it very difficult example) and approximate it by Bernstein operator.             

CONCLUSION:

Here, the important conclusions are that the compact set in real numbers is available best approximation element for any contra-continuous function which is located in it and the other is that the contra-continuous functions must be bounded.