For example, Ren and Wu [15] discussed the convergence of the secant method under

Holder continuous divided differences using a convergence ball.

The only difficulty is to show that the process [square root of V] is

Holder continuous of order H.

The requirements of continuity and robustness stand for a whole different problem when disturbance is

Holder continuous. The lack of integer-order differentiability of Holder functions suggests the design of fractional-order control since such functions exhibit well-posed derivatives just for some fractional orders.

In other words, almost every sample path of [??](t) is locally but uniformly

Holder continuous with exponent v.

Assumptions like partially Lipschitz and linear growth, [alpha]-inverse

Holder continuous or inverse Lipschitz, non-Lipschitz but bounded were used (see [16, 21, 22]).

The case when f is of bounded variation and u

Holder continuousBy [C.sup.0,[alpha]](S) and [c.sup.0,[alpha].sub.T] (S) we denote the spaces of

Holder continuous functions and

Holder continuous tangential fields (0 < [alpha] < 1), respectively.

where k is a non-negative, bounded and

Holder continuous function such that

The authors show that solutions of large classes of subelliptic equations with bounded measurable coefficients are

Holder continuous. They present two types of results for such equations: results that generalize the Fefferman-Phong geometric characterization of subellipticity in the smooth case and results that generalize a case of Hormander's algebraic characterization of subellipticity for sums of squares of real analytic vector fields.

Corollary 4.8 Let X have a bounded density [f.sub.X], which is

Holder continuous with exponent [alpha] [member of] (0,1].

Furthermore, we have that d[[micro].sub.w] (x) = f (x) dx, where f [member of] [C.sup.[infinity]] (U.sup.L.sub.l=1] ([a.sub.l],[b.sub.l])) and f is

Holder continuous on [S.sub.w] with exponent 1/2.

The technique we use here is well-known as the Bishop 1/4-3/4 method, but we include the details because we will sharpen them in section 5 to obtain

Holder continuous peak functions.