The author applies his general theory of computability depending on codings [ibid. 26, 565-576 (1980; Zbl 0455.03025), 27, 473-480 (1981; Zbl 0473.03051), 28, 377-383 (1982; Zbl 0509.03033)] to the set \(C<0,1>\) of continuous functions of the unit interval and some of its subsets. Three types of codings \(D^ 1\), \(D^ 2\), \(D^ 3\) are introduced, suitable for: \(C<0,1>\) and subsets \(C_ 1<0,1>\) of functions having at least one zero, \(C_ 2<0,1>\) of functions which are in no subinterval identically zero and for which \(f(0)f(1)<0, C'<0,1>\) of functions that are continuously differentiable.
A choice of results: A functional which assigns to f a zero is \(D^ 1\)- computable in \(C_ 2<0,1>\), \(D^ 2\)-computable in \(C_ 1<0,1>\), bot not \(D^ 1\)-computable in \(C_ 1<0,1>\). The operators \(Sup(f)=\sup f<0,1>\) and S, which assigns to f a modulus of continuity are \(D^ 1\)- computable on \(C<0,1>\). The operator \(A(f)=f'\) is not \(D^ 1\)-computable on \(C'<0,1>\), it is however \(D^ 3\)-computable. The integral operator I(f) is \(D^ 1\)-computable on \(C<0,1>\), and the Riemann-Stieltjes operator I(f,g) is \(D^ 3\)-computable on \(C<0,1>\times C'<0,1>\), but not \(D^ 1\)-computable.