Sentence examples for for a nondecreasing function from inspiring English sources

for a nondecreasing function such that (1.4).

It follows from condition (I) that begin{aligned} lim_{n toinfty} d( x_{n}, T x_{n}) geqlim _{n toinfty} fbigl( Dbigl(x_{n}, F(T bigr bigr), end{aligned} for a nondecreasing function (f [0, infty) to[0, infty)) with (f(0) = 0), (f(t) > 0 ) for all (t in 0, infty)).

For a (nondecreasing) function (phi: [0,+infty )rightarrow [0,+infty )), let us define the ϕ-variation of (f:[a,b]rightarrow W) as V^{phi} bigl f,[a,b]bigr):=sup_{n}sup _{ale t_{0}< t_{1}< cdots < t_{n}le b} sum_{i=1}^{n} phi bigl( biglVert f (t_{i} )-f (t_{i-1} ) bigrVert _{W} bigr).

Since for, is a nondecreasing function of that attains its maximum, for each fixed, when.

A function is called a m on if for all and all, for ; if and only if for all ; if ; ; is a nondecreasing function of and ; for, is continuous on.

A function is called a fuzzy norm on if for all and all, for ; if and only if for all ; if ; ; is a nondecreasing function of and ; for, is continuous on.

Let, For any fixed is a nondecreasing function with respect to, and for, following inequalities hold:, If, then for all.

For any fixed is a nondecreasing function with respect to, and for, the following inequalities hold: (2.5).

Let be a nondecreasing function with, for, and, for ; here, for.

Let be a -distance such that is l.s.c. on for each and be a nondecreasing function.

there exists a nondecreasing function with for each such that for, (3.22).