Sentence examples for be generalized to cyclic from inspiring English sources

If we assume that the function satisfies either of the conditions (i) or (ii) of Lemma 2.2, then all three theorems (Theorems, 11, and 12 of [3] can be generalized to cyclic -contraction maps. We omit the details. The next theorem generalizes Theorem 1.1 to reflexive Banach spaces. Note that if and for some fixed, then will be a cyclic contraction map, because for all and all we have (2.13).

This theory is generalized to continuous structures.

"His claims were tailored to be generalized," said Jenner.

But NNG's Tamas Kerecsen says those solutions are too generalized to be effective in vehicles.

The material law proposed previously was extended to cyclic loading.

Let T : A ∪ B → A ∪ B be a generalized cyclic contraction, that is, there exists r ∈ [ 0, 1 ) such that d ( T x, T y ) ≤ r max { d ( x, y ), d ( x, T x ), d ( y, T y ) } + ( 1 − r ) dist ( A, B ) (2). for all x ∈ A and y ∈ B. Then T has a unique best proximity point z in A, and for every x ∈ A the sequence { T 2 n x } converges to z.

Theorem 2.1 Let ( X, ≤ ) be a partially ordered set and ( X, F, Δ ) be a complete N.A Menger PM-space of type ( D ) g. Let m be a positive integer, A 1, A 2, …, A m be subsets of X, Y = ⋃ i = 1 m A i, T : Y → Y be a generalized cyclic ( κ h, φ L ) S -weak contraction satisfying (2.1).

Theorem 10 Let { A i } i = 1 k be nonempty closed subsets of a complete metric space (X, d), let φ : ℝ+ → ℝ+ be a φ-mapping in X, and let f : c u p i = 1 k A i → ∪ i = 1 k A i be a generalized cyclic weaker Meir-Keeler φ -contraction.

The 'reaction' cannot be rendered to be cyclic, nor autocatalysis.

( S, T ) is a generalized cyclic contraction.

(c) ( S, T ) is a generalized cyclic contraction.  .