Sentence examples for continuity of mapping from inspiring English sources

This contradiction proves the continuity of mapping.

The Banach contractive condition implies the continuity of mapping f.

With the help of the continuity of mapping function, spectrum values other than can be also obtained.

Moreover, the continuity of mapping (xrightarrow nu (x,cdot )) is necessary only in the strong case but not for the weak maximum principle.

Motivated by this approach, the digital continuity of maps between digital images was represented as follows.

The continuity of maps in a minimal space is defined as follows.

We obtain the following corollaries of Theorem 5 which improve Theorem 4.5 [4] by considering orbital continuity of maps and orbitally complete space instead of continuity of maps on complete space.

By the sequentially fuzzy continuity of maps and, we can find some such that for any, (3.40).

To map every (k_{0} -connected subset of ((X, k_{0} -connectedk_{1})-connected subset of ((Y, k_{1})), the paper [13] established the notion of digital continuity of maps between digital images.

Omitting the continuity assumption of mapping T or S in Theorem 1, modifying the contraction condition (3.1) and imposing on a comparison function φ a corresponding condition, then we can prove the following theorem.

Remark 3.1 Note that the Corollary 3.3 is a proper extension of the contraction mapping principle [13] because the continuity of the mapping T is not required.