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

So there is natural and essential to study existence of fixed points in the setting of locally convex spaces.

Now, we state and prove the uniqueness of fixed points in the setting of a complete partially ordered metric space.

One can find the existence of coupled fixed points in the setting of partially order metric space in [18 24].

The aim of this paper is to define some new conditions of common contractivity for an infinite family of mappings and give some new results on the existence and uniqueness of common fixed points in the setting of complete metric space.

Motivated by the above theorems, we introduce the concept of the proximal mixed monotone property and of a proximally coupled weak contraction on A. We also explore the existence and uniqueness of coupled best proximity points in the setting of partially ordered metric spaces.

Several years later, the theory of coupled fixed points in the setting of an ordered metric space and under some contractive type conditions on the operator T was re-considered by Gnana Bhaskar and Lakshmikantham in [16] (see also Lakshmikantham and Ćirić in [17]).

For completeness, let us state the definition of an extremal point in the setting of -trees.

Also one can find the existence of best proximity point in the setting of partially order metric space in [14 17].

Other known results of fixed point in the setting of partial metric spaces we can get considering suitable simulation functions.

In 2012, Colao et al. [8] first established the existence for an equilibrium point in the setting of Hadamard manifolds.

For the existence of a best proximity point in the setting of partially ordered metric spaces, see [9 13].