Sentence examples for bounded variation defined on from inspiring English sources

Here (operatorname{BV}(mathbb{Z}^{d})) represents the set of functions of bounded variation defined on (mathbb{Z}^{d}).

where BV is the space of functions of bounded variation defined on Ω, and μ > 0 is a parameter to be chosen.

We also denote by (operatorname{BV}(mathbb{Z}^{d})) the set of all functions of bounded variation defined on (mathbb{Z}^{d}), where the total variation of (f:mathbb{Z}^{d}rightarrowmathbb{R}) is defined by operatorname{Var}(f)=sum_{l=1}^{d} Vert D_{l}f Vert _{ell ^{1}(mathbb{Z}^{d})}.

Let and be any real functions of bounded variation and defined, respectively, on the intervals and of the extended real line.

In 2009, Karsli et al. [2] gave an estimate of the rate of pointwise convergence of the operators (1) on a Lebesgue point of a bounded variation function f defined on the interval ( 0, ∞ ).

Functions of bounded variation (BV functions) are defined on an abstract Wiener space (E, H, μ) in a way similar to that in finite dimensions.

If is a continuous function of bounded variation on, then one has the inequality (1.4).

It is related to the class of functions with bounded Mocanu variation defined by Coonce and Ziegler [6] and intensively investigated by Noor et al. [24 27].

Theorem A. Let be a function of bounded variation on,, then for every and one has.

(i) Let C be a bounded variation function on Γ.

Let f be a function of bounded variation on [ a, b ], and let V be a function defined by V ( x ) = V x b ( f ).