Sentence examples for boundedness of a linear from inspiring English sources

Bag and Samanta [5] introduced a notion of boundedness of a linear operator between fuzzy normed spaces, and studied the relation between fuzzy continuity and fuzzy boundedness.

The main result on the boundedness of solutions of a linear Volterra difference system in [2] was improved by Györi and Horváth [8].

The above fact and the closed graph theorem imply the boundedness of the linear operator A B − 1 : Y → Y.

The hypotheses H 1, H 2 and the closed graph theorem imply the boundedness of the linear operator A E − 1 : Y → Y. ( H 4 ) For each t ∈ [ 0, a ] and for some λ ∈ ρ ( − A E − 1 ), the resolvent set of − A E − 1, the resolvent R ( λ, − A E − 1 ) is a compact operator.

They studied boundedness of linear operators over fuzzy normed linear spaces such as fuzzy continuity, sequential fuzzy continuity, weakly fuzzy continuity and strongly fuzzy continuity.

To the best of our knowledge, this is the first article dealing with the boundedness property of the solutions of a linear inhomogeneous Volterra difference system with the critical case ∑ i = 0 ∞ | | A ( i ) | | = 1.

which implies the boundedness of the linear transformation.

Then the boundedness of linear operators in Hardy-type spaces can be deduced from their behavior on atoms in principle.

We obtain conditions for the boundedness of linear operators on these distribution spaces by considering corresponding conditions for matrices on the associated sequence spaces.

Boundedness of solutions of linear discrete Volterra equations has been studied by many authors.

Boundedness of solutions of linear and nonlinear discrete Volterra equations was also studied by Crisci et al. [7], Diblík and Schmeidel [8], Gronek and Schmeidel [9], Győri and Awwad [10], Győri and Horváth [11], Kolmanovskii and Shaikhet [1], Medina [12], Migda and Migda [13] or Migda and Morchało [14].