For example, Ren and Wu  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 continuous
By [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