forward difference operator

forward difference operator

[¦fȯr·wərd ¦dif·rəns ′äp·ə‚rād·ər]
(mathematics)
A difference operator, denoted Δ, defined by the equation Δƒ(x) = ƒ(x + h) - ƒ(x), where h is a constant indicating the difference between successive points of interpolation or calculation.
References in periodicals archive ?
The forward difference operator is denoted by [DELTA].
We call [f.sup.[DELTA]](t) the delta (or Hilger) derivative of f(t) and it turns out that [f.sup.[DELTA]] is the usual derivative if T = R and is the usual forward difference operator if T = Z.
One can check that in these cases we have [f.sup.[DELTA]](t) = f'(t), [f.sup.[DELTA]](t) = [[DELTA].sub.[omega]] f(t) and [f.sup.[DELTA]](t) = [D.sub.q] f(t), respectively, where [[DELTA].sub.[omega]] f(t) = f (t + [omega]) - f(t) / [omega] is the forward difference operator with stepsize [omega] [32], and [D.sub.q] f(t) = f(qt) - f(t) / t(q - 1) (for t [not equal to] 0) is the q-difference operator [10].
The second important problem which cannot be obtained from the calculus of time scales, concerns the forward difference operator
where f, g : N([n.sub.0]) x R x R [right arrow] R, N([n.sub.0]) = {[n.sub.0], [n.sub.0] + 1, [n.sub.0] + 2, ...} ([n.sub.0] a nonnegative integer, x([n.sub.0]) = [x.sub.0], y([n.sub.0]) = [y.sub.0]), and [DELTA] denotes the forward difference operator, that is, [DELTA]x(n) = x(n +1) - x(n) for a sequence x(n).
In this section, we give a theorem which provides some estimates on these type of the inequality (2) about the forward difference operator.