Sentence examples for bounded subsets of the from inspiring English sources

We will denote by the family of all subsets of the family of nonempty closed and bounded subsets of the family of nonempty compact subsets of.

We establish some fixed point theorems for multi-valued mappings from a complete metric space to the space of closed or bounded subsets of the metric space satisfying generalized -contractive condition.

Using the notion of a partial metric on a set X, Aydi et al. [18] defined a partial Hausdorff metric on the set of closed and bounded subsets of the set X.

As in [21, 22, 24], let (C_{b}(X)) be the family of all nonempty, closed and bounded subsets of the b-metric-like space ((X,sigma)), induced by the b-metric-like σ.

For any 0 < α < β < 1, 0 ≤ p ≤ q, the bounded subsets of the space C q + β ( Q T ) are precompact subsets of C p + α ( Q T ).

We will use the following notations, throughout this paper, where is a symmetric space, and, and is the class of all nonempty bounded subsets of The diameter of is denoted and defined by.

If is a bounded subset of, the Chebyshev radius of relative to is defined by (2.4).

Suppose that for each bounded subset of, the ordered pair satisfies either condition AKTT or condition.

Then Ω is an open and bounded subset of the Banach space C 1 [ 0, T ].

Clearly, S is a closed, convex, and bounded subset of the Banach space X.

Suppose that for each bounded subset of, the ordered pair satisfies condition AKTT.