Approximation in Real Contra-Continuous Functions Spaces

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.