Sentence examples for valued case from inspiring English sources

Now let us begin with the convex valued case.

Also Žikić generalized multi valued case of Hick's contraction [8].

The first one concerns the convex valued case, and the others are related to the nonconvex valued case.

We extended (φ - k) - B contraction which introduced by Mihet [9] to multi valued case [10].

Now, we obtain two fixed-point theorems of -contraction for single valued case.

On the other hand, Hadzic et al. extended the concept of contraction to the multi valued case [5].

(a) Convex set-valued case.

Later, many researchers extended (EP) to the vector set-valued case in different ways; see [5 7] and the references therein.

This vector-valued (Banach space-valued) case is particularly important for applications to (the asymptotic behavior of solutions to) differential equations and dynamical systems.

(b) Nonconvex set-valued case.

All these inequalities hold equally in the vector-valued case, that is, for functions with values in ℓρ for 1<ρ<∞.