Sentence examples for mapping is uniformly from inspiring English sources

In 1973, Goebel and Kirk [3] introduced the class of uniformly -lipschitzian mappings, recall that a mapping is uniformly -lipschitzian,, if.

Moreover, an asymptotically nonexpansive mapping is uniformly L-Lipschitzian.

First, the mapping is uniformly distributed on the entire constellation.

We note that every asymptotically nonexpansive mapping is uniformly -Lipschitzian.

Similarly, from (3.29) and the duality mapping is uniformly continuous on bounded subset of, it follows that (3.48).

It is clear that every nonexpansive mapping is asymptotically nonexpansive and every asymptotically nonexpansive mapping is uniformly Lipschitzian.

Moreover, a uniformly L-Lipschitzian map is uniformly Hölder continuous, and a uniformly Hölder continuous map is uniformly equicontinuous.

If S or T is semi-compact, then { x n } converges strongly to a common fixed point of S and T. As every uniformly equicontinuous map is uniformly L-Lipschitzian, so the following result is immediate and it unifies Theorem 2.1 and Theorem 2.2 of Chang et al. [13] in Hadamard spaces.

Note that both coefficients of these affine maps are uniformly bounded from above in norm, and that.

Also, uniformly C q -commuting maps on X are C q -commuting and uniformly R-subweakly commuting maps are uniformly C q -commuting but the converse statements do not hold, in general [23, 25].

If E is a smooth Banach space, then the mapping J is single-valued; J ( α x ) = α J ( x ) for all x ∈ E and α ∈ ℜ ; If E is a uniformly smooth Banach space, then the mapping J is uniformly continuous on any bounded subset of E. We denote the single-valued normalized duality mapping by j.