Results 221 to 230 of about 43,776 (261)

ON FUNCTIONS OF BOUNDED $ p$-VARIATION

Mathematics of the USSR-Izvestiya, 1968
In this article we obtain an asymptotic formula for the approximations to functions in the class (, ) by Fourier sums in the metric of (). We find sufficient conditions and also criteria for the continuity of the derivative of a function in the class . We also give some results on the Fourier coefficients of functions in the above class.
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Functions of Bounded Variation

2015
We know that if f is integrable, then the lower and upper sums of every partition F approximate its integral from below and above, and so the difference between either sum and the integral is at most \(S_{F} - s_{F} =\varOmega _{F}\), the oscillatory sum corresponding to F.
Miklós Laczkovich, Vera T. Sós
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Omniscience Principles and Functions of Bounded Variation

MLQ, 2002
Omniscience principles are general statements that can be proved classically but not constructively. They are used to show that other, more subject-specific statements that imply some omniscience principle do not have a constructive proof. The strongest omniscience principle is the law of excluded middle itself.
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ITERATED FUNCTION SYSTEMS ON FUNCTIONS OF BOUNDED VARIATION

Fractals, 2016
We show that under certain hypotheses, an iterated function system on mappings (IFSM) is a contraction on the complete space of functions of bounded variation (BV). It then possesses a unique attractor of BV. Some BV-based inverse problems based on the Collage Theorem for contraction maps are considered.
D. La Torre, F. Mendivil, E. R. Vrscay
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Composing Functions of Bounded ϕ-Variation

Proceedings of the American Mathematical Society, 1986
Functions of bounded \(\phi\)-variation appeared first in a paper of \textit{N. Wiener} [Massachusetts J. Math. 3, 72-94 (1924)]. Afterwards it was studied by others leading to generalizations and different perspectives. A \(\phi\)-function what is understood as far as this paper is concerned is a continuous, unbounded, non-decreasing function on \([0,\
Ciemnoczołowski, J., Orlicz, W.
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Nonconservative Products in Bounded Variation Functions

SIAM Journal on Mathematical Analysis, 1992
Summary: There exist two definitions of products of a bounded variation function by a derivative of another bounded variation function. One of them follows from a concept of generalized functions in which arbitrary products of distributions make sense: one has only one product but its understanding involves a nonclassical concept contained in each ...
Colombeau, Jean François, Heibig, Arnaud   +1 more
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Minimizing Functions with Bounded Variation of Subgradients [PDF]

SSRN Electronic Journal, 2005
In many applications it is possible to justify a reasonable bound for possible variation of subgradients of objective function rather than for their uniform magnitude. In this paper we develop a new class of efficient primal-dual subgradient schemes for such problem classes.
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On Superposition of Functions of Bounded ϕ-Variation

Proceedings of the American Mathematical Society, 1989
A function \(\phi\) : [0,\(\infty)\to [0,\infty)\) is called a \(\phi\)- function if it is continuous, non-decreasing and such that \(\phi (0)=0\), \(\phi (u)>0\) for \(u>0\) and \(\phi\) (u)\(\to \infty\) as \(u\to \infty\). For a \(\phi\)-function \(\phi\) and a real function F defined on (- \(\infty,\infty)\) it is said that \(F\in GL_{\phi}\) if ...
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FUNCTIONS OF BOUNDED GENERALIZED SECOND VARIATION

Mathematics of the USSR-Sbornik, 1980
This paper introduces the classes and of functions of variables. These classes, for , are more general than the class of functions of bounded second variation introduced by F.I. Harsiladze, and in the case they contain the classes of functions of bounded generalized variation introduced by B.I. Golubov.
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On the Decomposition of A Class of Functions of Bounded Variation

Canadian Journal of Mathematics, 1964
Let F1(x) and F2(x) be two distribution functions, that is, non-decreasing, right-continuous functions such that Fj(— ∞) = 0 and Fj(+ ∞) = 1 (j = 1, 2). We denote their convolution by F(x) so thatthe above integrals being defined as the Lebesgue-Stieltjes integrals. Then it is easy to verify (2, p. 189) that F(x) is a distribution function.
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