Sentence examples for extended in the setting of from inspiring English sources

The geometric derivation is then extended in the setting of generalized or continuous frames.

The inequality (28) was extended in the setting of a totally real submanifold in a quaternionic space form by Liu and Dai in [51] and recently, in [52], both inequalities (28) and (29) were generalized for proper slant submanifolds in quaternionic space forms as follows.

It is worth emphasizing that the nonexpansive mapping T in (1.5) is extended to a ξ-strictly pseudocontractive mapping T in (3.1) and the VIP in SHVI (1.6) is extended to the setting of finitely many GMEPs and finitely many variational inclusions in SHVI (1.10).

Moreover, F ( T ) = { x ∈ Y : T x = x } will be denoted as the set of fixed points of T : Y → X. Approximately, all the concepts and results in metric spaces are extended to the setting of b-metric spaces (for more details, see [1]).

This set of scenarios will be extended in the course of the project, but we will try to make the set of scenarios as small as possible in order to avoid overwhelming the teacher.

The concept of commutativity of single-valued mappings [13] was extended in [14] to the setting of a single-valued mapping and a multi-valued mapping on a metric space.

The main Ascoli-type results given in [35] have been extended in the lattice group setting and in the context of filter convergence and exhaustiveness (and also a concept similar to 'total boundedness' has been presented in terms of filters), giving some compactness result again with respect to uniform convergence on compact sets.

Matthews [1] introduced the notion of a partial metric space and extended Banach contraction principle in the setting of partial metric space.

Holland, in truth, were not fully extended in the qualifiers but a complete set of eight victories demonstrated powers of concentration.

Taking ψ ( t ) = t and φ ( t, u ) = 1 ( s + 1 ) a − 1, a ∈ ( 0, 1 ) in Theorem 3.3, an extended Kannan fixed point theorem in the setting of b-metric spaces has been obtained.

Moreover, they [18] extended Nadler's fixed point theorem in the setting of a partial Hausdorff metric spaces.