Results 31 to 40 of about 548,657 (153)

Riemann–Liouville Fractional Sobolev and Bounded Variation Spaces

Axioms, 2022
We establish some properties of the bilateral Riemann–Liouville fractional derivative Ds. We set the notation, and study the associated Sobolev spaces of fractional order s, denoted by Ws,1(a,b), and the fractional bounded variation spaces of fractional ...
Antonio Leaci, Franco Tomarelli
doaj   +1 more source

Nonlocal Bounded Variations with Applications

SIAM Journal on Mathematical Analysis
Motivated by problems where jumps across lower dimensional subsets and sharp transitions across interfaces are of interest, this paper studies the properties of fractional bounded variation ($BV$)-type spaces. Two different natural fractional analogs of classical $BV$ are considered: $BV^α$, a space induced from the Riesz-fractional gradient that has ...
Harbir Antil, Hugo Díaz, Tian Jing, Armin Schikorra   +3 more
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Non-Autonomous Maximal Regularity for Forms of Bounded Variation [PDF]

, 2014
We consider a non-autonomous evolutionary problem \[ u' (t)+\mathcal A (t)u(t)=f(t), \quad u(0)=u_0, \] where $V, H$ are Hilbert spaces such that $V$ is continuously and densely embedded in $H$ and the operator $\mathcal A (t)\colon V\to V^\prime$ is ...
Dier, Dominik
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On Anisotropic $BV$-Spaces

Researches in Mathematics
This paper is devoted to the study of a new class of functional spaces, the so-called anisotropic $BV$-spaces with a degenerate weight. We give a precise definition of such spaces and show that they can be viewed as a natural generalization of the ...
P. Kogut
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Bounded variation of functions defined on a convex and compact set in the plane

Arab Journal of Basic and Applied Sciences, 2023
In this paper, the variation of functions has been defined, whose domain is a convex and compact set in the plane. Furthermore, in addition to presenting properties that satisfy this variation, the vector space formed by functions with finite variation ...
Mireya Bracamonte, Juan Tutasi
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A universal bound on the variations of bounded convex functions [PDF]

, 2015
Given a convex set $C$ in a real vector space $E$ and two points $x,y\in C$, we investivate which are the possible values for the variation $f(y)-f(x)$, where $f:C\longrightarrow [m,M]$ is a bounded convex function. We then rewrite the bounds in terms of
Kwon, Joon
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On Bounded Second Variation

Advances in Pure Mathematics, 2012
In this paper, we discuss various aspects of the problem of space-invariance, under compositions, of certain subclasses of the space of all continuously differentiable functions on an interval [a,b] We present a result about integrability of products of the form gοf.f'f(k)under suitable mild conditions and, finally, we prove that a Nemytskij operator ...
José Giménez, Lorena López, N. Merentes, J. L. Sánchez   +3 more
openaire   +1 more source

New Information Inequalities in Terms of Variational Distance and its Application

Journal of New Results in Science, 2016
In this work, new information inequalities are obtained and characterized on new generalized f- divergence (introduced by Jain and Saraswat (2012)) in terms of the Variational distance and these inequalities have been taken for evaluating some new ...
K. C. Jain, Praphull Chhabra
doaj  

Grüss–Ostrowski inequalities and bounded variation

Journal of Inequalities and Applications
In this note, we establish corresponding Grüss–Ostrowski-type inequalities for functions with bounded variation. As an application, we provide some estimates for the error in numerical integration rules and estimation for the cumulative distribution ...
Karol Gryszka
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Multifunctions of Bounded Variation, Preliminary Version I [PDF]

, 2015
Consider control systems described by a differential equation with a control term or, more generally, by a differential inclusion with velocity set $F(t,x)$.
Vinter, R. B.
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