Sentence examples for strong metric from inspiring English sources

If this assumption fails, the equivalence between the strong metric subregularity and the strong metric regularity may be a failure.

Our study is focused on two key notions: metric subregularity and strong metric subregularity.

This work is devoted to studying the relationships among strong metric subregularity, the quadratic growth condition, strong metric regularity, and the positive-definiteness property of the second-order subdifferential/generalized Hessian in finite and infinite-dimensional settings.

Under the assumptions of Theorem 4.2, we see that the constant c in the quadratic growth condition (1) can attain to (frac{1}{kappa}), and the strong metric subregularity is equivalent to the strong metric regularity.

In the following theorem, we establish an equivalence among the strong metric subregularity, the quadratic growth condition, the positive-definiteness property of the second-order subdifferential/generalized Hessian, the strong metric regularity, and tilt stability for a proper l.s.c.

(i) Under the assumptions of Theorem 4.2, we see that the constant c in the quadratic growth condition (1) can attain to (frac{1}{kappa}), and the strong metric subregularity is equivalent to the strong metric regularity.

And M in this case is said to be a strong fuzzy metric on X.

In the following theorems conditions (34) and (47) proposed in [32] are used to obtain fixed point results in complete and compact strong fuzzy metric spaces.

Let ((X, M, T) ) be a complete strong fuzzy metric space with positive t-norm T and let (f : X to X).

Let ((X, M, T) ) be a compact strong fuzzy metric space and let (varphi: [0,1] rightarrow[0,1] ) satisfying conditions (AD1) and (AD2) such that varphibigl(T r, s bigr) leqvarphi(r) + varphi(s),quad r, s inbigl{ M x, fx, t): x in X, t > 0bigr}.

In Section 2 the definitions of a dislocated (strong quasi- metric and of a partial metric are presented.