Sentence examples for instead of continuity from inspiring English sources

While earlier forms prioritized a relatively smooth interface of melodic elements, sonata form emphasizes conflict instead of continuity, ultimately deriving its impact from the explosive power of tonal organization.

Corollary 2.2 Assume the conditions (25) and (26) instead of continuity of F in Corollary  2.1, then the conclusion of Corollary  2.1 holds.

Theorem 2.2 Assume the conditions (25), (26) and A 0 is closed in X instead of continuity of F in Theorem  2.1, then the conclusion of Theorem  2.1 holds.

To prove T z = z, instead of continuity of T, using (3.3) we have ∥ T x m − T z ∥ ≤ m ( x m, z ) + L n ( x m, z ), (3.4).

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.

Then (overline{mathrm{O}} -completeness O}} -completenessexistence of (zin X) such that g(x_{n})uparrow z quadmbox{and}quad f(x_{n})uparrow z. (2) Owimplies(2), we use (overline{mathem{O}})-continuity and (ovexistencethrm{of})-compatibility instead of continuity and O-compatibility.

In Definition 1.1, we assume the continuity of T instead of uniform continuity.

In this article, we assume the continuity of T instead of uniform continuity.

Remark 1 If we assume that α has (B) property instead of the continuity of T, then again T has a fixed point (Theorem 2.2 of [13]).

Therefore in the next result, instead of complete continuity of mappings T 1, T 2, …, T N, we use condition ( C ¯ ).

Theorem 45 If, instead of G-continuity of F in the theorem above, we assume that X is ordered complete, then F has a coupled fixed point.