h-monotonically computable real numbers
G. Barmpalias, R. Rettinger and X. Zheng
Summary
Let h be a computable function from the natural number to the rational numbers.
A real number x is called h-monotonically computable (h-mc, for
short) if there is a computable sequence (x(s) ) of rational numbers which converges to x
h-monotonically in the
sense that the distance of x from x(m) over the distance of x from x(n) is less than h(n)
for all m>n.
In this paper we investigate classes of h-mc
real numbers for different computable functions h.