Sentence examples for be a -cyclic contraction from inspiring English sources

Let  be a -cyclic contraction of Meir-Keeler type.

let be a -cyclic -contraction self-mapping, then, (3.2). (3.3).

The following properties hold: (i) let be a -cyclic -contraction self-mapping, then, (3.2) (3.3) where ;.

Thus, if is a -cyclic -contraction, then it is also a contraction of Meir-Keeler type (3.27).

Then, since is a -cyclic -contraction, one gets that (3.28).

Since is a -cyclic -contraction, then it is -cyclic nonexpansive so that ;.

Consider the self-mapping, subject to ;,, and assume that and ; so that is a -cyclic -contraction.

Then, is a -cyclic -contraction self-mapping if ; with ; and, furthermore, (3.1).

It turns out that such a mapping is a -cyclic -contraction if the composed self-mappings on are composed -cyclic -contractions.

Theorem 2.1 Let A and B be nonempty subsets of a metric space ( X, d ) and T : A ∪ B → A ∪ B be an MT -cyclic contraction with respect to φ.

Theorem 3.1 Let A and B be nonempty subsets of a metric space ( X, d ) and T : A ∪ B → A ∪ B be an MT -cyclic contraction with respect to α.