Sentence examples for a cyclic map from inspiring English sources

Suppose f : A ∪ B → A ∪ B is a cyclic map such that for some x ∈ A, there exists a φ-mapping φ : ℝ+ → ℝ+ in X such that d ( f 2 n x, f y ) ≤ φ ( d ( f 2 n - 1 x, y ) ), n ∈ ℕ, y ∈ A. (3).

Suppose f : A ∪ B → A ∪ B is a cyclic map such that for some x ∈ A, there exists a ψ-mapping ψ x : R + → R + in X such that d ( f 2 n x, f y ) ≤ ψ x ( d ( f 2 n − 1 x, y ) ), for all n ∈ N and y ∈ A. Then f is called a cyclic orbital weaker Meir-Keeler ψ x -contraction.

Suppose that is a cyclic map such that (1.1).

We begin with the definition of a cyclic map.

f is a cyclic map; f is continuous.

f is a cyclic map; X satisfies property (P).

Let T be a cyclic mapping that satisfies the condition of a dqb-cyclic-Kannan mapping.

Let T be a cyclic mapping that satisfies the condition of a dqb-cyclic-Banach contraction.

Suppose that T : A ∪ B → A ∪ B is a cyclic mapping.

Finally, we apply our main results for proving a fixed point theorem involving a cyclic mapping.

We apply our main results for proving a fixed point theorem involving a cyclic mapping.