Sentence examples for mappings and show from inspiring English sources

In the following subsections, we review the pertinent results on the fixed point theory of Lipschitz mappings and show the relationship with the fixed point theory of the higher-order counterparts as introduced above.

In this paper we deal with stationary points (also known as endpoints) of nonexpansive set-valued mappings and show that the existence of such points under certain conditions follows as a consequence of the existence of approximate stationary sequences.

In this paper we do not consider more general spaces, but instead we formulate less restrictive conditions for the mappings and show that the conclusions of the theorems still stand even in such weaker settings.

We propose a new class of nonlinear mappings, called ( a, b ) -monotone mappings, and show that this class of nonlinear mappings contains nonspreading mappings, hybrid mappings, firmly nonexpansive mappings, and ( a 1, a 2, a 3, k 1, k 2 ) -generalized hybrid mappings with a 1 < 1.

For instance, Rakotch [2] introduced the class of contractive mappings and showed that their iterates also converged to their unique fixed point.

First, we establish the result on points of coincidence and common fixed points for three self-mappings and then show that this result generalizes some of recent results of fixed point.

In order to do so, we first show the connection between isotone mappings and acyclic mappings before showing the relationship between fixed points and the cyclicity of the mapping.

The SEM insets and EDS mappings show good matching and the MDs are indeed consisted of Ga as clearly shown in Figure 3 (a-2) and (b-2).

By a simple computation, one can show that the mappings and satisfy the functional equation (1.6), so the mapping f satisfies (1.6).

They all considered one mapping or a pair of commuting mappings to show the existence of invariant approximation.

The TEM images and oxygen and tungsten mappings are shown in Figure 2. Nanorods with diameters of about 10 to 20 nm and various lengths were confirmed in the TEM image in Figure 2a.