Sentence examples for be a complete S-probabilistic from inspiring English sources

Let ((E, F)) be a complete S-probabilistic metric space.

Theorem 2.2 Let ( E, F ) be a complete S-probabilistic metric space.

We denote by x = P y the P-operator from B 0 into  A 0. Theorem 3.1 Let ( E, F ) be a complete S-probabilistic metric space.

This shows that (PT: A_{0} rightarrow A_{0}) is a contraction from a complete S-probabilistic metric subspace (A_{0}) into itself.

From (2.7) we know that ({x_{n}}) is a Cauchy sequence in a complete S-probabilistic metric space ((E,F)).

holds for all n ≥ 1. Proof Since the pair ( A, B ) has the weak P-property, we have F P T x 1, P T x 2 ( t ) ≥ F T x 1, T x 2 ( t ) ≥ F x 1, x 2 ( t h ), ∀ t > 0, for any x 1, x 2 ∈ A 0. This shows that P T : A 0 → A 0 is a contraction from complete S-probabilistic metric subspace A 0 into itself.

Let ((E, F, triangle )) be a complete Menger probabilistic metric space.

Let ((E, F, mathrm{min})) be a complete Menger probabilistic metric space.

Theorem 2.3 Let ( E, F, △ ) be a complete Menger probabilistic metric space.

Let ((E, F, triangle_{2})) be a complete Menger probabilistic metric space, where (triangle_{2}(a,b =acdot b).

Let ( E, F, △ ) be a complete Menger probabilistic metric space for which the triangular norm △ is continuous and satisfies △ ( a, b ) = min ( a, b ).