Search results for " continuity."
showing 10 items of 229 documents
THE HKr-INTEGRAL IS NOT CONTAINED IN THE Pr-INTEGRAL
2022
We compare a Perron-type integral with a Henstock-Kurzweiltype integral, both having been introduced to recover functions from their generalized derivatives defined in the metric Lr. We give an example of an HKr-integrable function which is not Pr-integrable, thereby showing that the first integral is strictly wider than the second one.
AN ADDENDUM TO: A COMMON FIXED POINT THEOREM IN INTUITIONISTIC FUZZY METRIC SPACE USING SUBCOMPATIBLE MAPS"
2012
The aim of this note is to point out a fallacy in the proof of Theorem 3.1 contained in the recent paper ( Int. J. Contemp. Math. Sci. 5 (2010), 2699-2707) proved in intuitionistic fuzzy metric spaces employing the newly introduced notion of sub-compatible pair of mappings wherein our claim is also substantiated with the aid of an appropriate example. We also rectify the erratic theorem in two ways.
Regular subclasses in the Sobolev space W_{loc}^{1,n}
2009
Westudy some slight modifications of the class AC^n introduced in [D. Bongiorno, Absolutely continuous functions in Rn, J. Math. Anal. and Appl. 303 (2005) 119 134]. In particular we prove that the classes introduced in [C. Di Bari, C. Vetro, A remark on absolutely continuous functions in R^n, Rend. Circ. Matem. Palermo 55 (2006) 296 304] are independent by and contain properly the class AC^n.
Estimates of maximal functions measuring local smoothness
1999
Letη be a nondecreasing function on (0, 1] such thatη(t)/t decreases andη(+0)=0. Letf ∈L(I n ) (I≡[0,1]. Set $${\mathcal{N}}_\eta f(x) = \sup \frac{1}{{\left| Q \right|\eta (\left| Q \right|^{1/n} )}} \smallint _Q \left| {f(t) - f(x)} \right|dt,$$ , where the supremum is taken over all cubes containing the pointx. Forη=t α (0<α≤1) this definition was given by A.Calderon. In the paper we prove estimates of the maximal functions $${\mathcal{N}}_\eta f$$ , along with some embedding theorems. In particular, we prove the following Sobolev type inequality: if $$1 \leqslant p< q< \infty , \theta \equiv n(1/p - 1/q)< 1, and \eta (t) \leqslant t^\theta \sigma (t),$$ , then $$\parallel {\mathcal{N}}_…
On the Hencl's notion of absolute continuity
2009
Abstract We prove that a slight modification of the notion of α-absolute continuity introduced in [D. Bongiorno, Absolutely continuous functions in R n , J. Math. Anal. Appl. 303 (2005) 119–134] is equivalent to the notion of n, λ-absolute continuity given by S. Hencl in [S. Hencl, On the notions of absolute continuity for functions of several variables, Fund. Math. 173 (2002) 175–189].
$L_2$-variation of L\'{e}vy driven BSDEs with non-smooth terminal conditions
2016
We consider the $L_2$-regularity of solutions to backward stochastic differential equations (BSDEs) with Lipschitz generators driven by a Brownian motion and a Poisson random measure associated with a L\'{e}vy process $(X_t)_{t\in[0,T]}$. The terminal condition may be a Borel function of finitely many increments of the L\'{e}vy process which is not necessarily Lipschitz but only satisfies a fractional smoothness condition. The results are obtained by investigating how the special structure appearing in the chaos expansion of the terminal condition is inherited by the solution to the BSDE.
Applications de type Lasota–Yorke à trou : mesure de probabilité conditionellement invariante et mesure de probabilité invariante sur l'ensemble des …
2003
Abstract Let T :I→I be a Lasota–Yorke map on the interval I, let Y be a nontrivial sub-interval of I and g 0 :I→ R + , be a strictly positive potential which belongs to BV and admits a conformal measure m. We give constructive conditions on Y ensuring the existence of absolutely continuous (w.r.t. m) conditionally invariant probability measures to nonabsorption in Y. These conditions imply also existence of an invariant probability measure on the set X∞ of points which never fall into Y. Our conditions allow rather “large” holes.
Can the Adaptive Metropolis Algorithm Collapse Without the Covariance Lower Bound?
2011
The Adaptive Metropolis (AM) algorithm is based on the symmetric random-walk Metropolis algorithm. The proposal distribution has the following time-dependent covariance matrix at step $n+1$ \[ S_n = Cov(X_1,...,X_n) + \epsilon I, \] that is, the sample covariance matrix of the history of the chain plus a (small) constant $\epsilon>0$ multiple of the identity matrix $I$. The lower bound on the eigenvalues of $S_n$ induced by the factor $\epsilon I$ is theoretically convenient, but practically cumbersome, as a good value for the parameter $\epsilon$ may not always be easy to choose. This article considers variants of the AM algorithm that do not explicitly bound the eigenvalues of $S_n$ away …
Existence, uniqueness and Malliavin differentiability of Lévy-driven BSDEs with locally Lipschitz driver
2019
We investigate conditions for solvability and Malliavin differentiability of backward stochastic differential equations driven by a L\'evy process. In particular, we are interested in generators which satisfy a locally Lipschitz condition in the $Z$ and $U$ variable. This includes settings of linear, quadratic and exponential growths in those variables. Extending an idea of Cheridito and Nam to the jump setting and applying comparison theorems for L\'evy-driven BSDEs, we show existence, uniqueness, boundedness and Malliavin differentiability of a solution. The pivotal assumption to obtain these results is a boundedness condition on the terminal value $\xi$ and its Malliavin derivative $D\xi…
On Limiting Fréchet ε-Subdifferentials
1998
This paper presents an e-sub differential calculus for nonconvex and nonsmooth functions. We extend the previous work by Jofre et all to the case where the functions are lower semicontinuous instead of locally Lipschitz.