Suppose that there exists a nonnegative rd-continuous

bounded function p(t) such that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], for all t [member of] T and some positive number [[lambda].

R] in the approximation of a continuous, positive and

bounded function f on R.

Suppose f is a

bounded function in [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] Then there exist C < [infinity] and a fixed scale [a.

GAMMA]]f > 0, where [GAMMA] is a

bounded function on the interval I = (a, b).

Further, we assume that p(x, y) is a strictly positive function and q(x, y) is a nonnegative smooth

bounded function on [OMEGA].

G) for any

bounded function [epsilon], or equivalently for any choice of signs [epsilon] (x) = [+ or -] 1.

Therefore, without loss of generality, one may assume that there exists a

bounded function f(.

Consequently, M acts by multiplication with an essentially

bounded function [?

m]) be as in Lemma 1 and let f be a

bounded function in [Mathematical Expression Omitted].

v] (t) is a

bounded function on (0,[infinity]) also shows that in the case v [greater than or equal to] -1/2, [[phi].

It is assumed that F is a function class consisting of

bounded functions with the range [a, b].