Sentence examples for mappings we will from inspiring English sources

If ( X, ≼ ) is a preordered space and T, g : X → X are two mappings, we will say that T is a ( g, ≼ ) -nondecreasing mapping if T x ≼ T y for all x, y ∈ X such that g x ≼ g y.

Definition 3 If ( X, ≼ ) is a preordered space and T, g : X → X are two mappings, we will say that T is a ( g, ≼ ) -nondecreasing mapping if T x ≼ T y for all x, y ∈ X such that g x ≼ g y.

Since this work concerns the fixed point property of mappings, we will need the following property.

In order to extend this conclusion to a family of mappings, we will need the following definition.

Since in this work we discuss the fixed point theory of monotone mappings, we will need to introduce a partial order in ((X,d)).

Apart from continued fine-mapping, we will also use transcriptome sequencing and association mapping to confirm the candidate gene for qRgls2.

The class of nonlinear mappings which we will study is the class of pseudocontractions.

"By the end of our local-mapping campaign, we will be able to see an object the size of a penny on the surface of Bennu," Daniella DellaGiustina, the mission's lead image-processing scientist, said.

Given two mappings (f,g Xrightarrow X), we will say that the pair ({ f,g}) is (( alpha,d ) ) -regular if max bigl{ alpha ( x_{n},u ),alpha ( u,x_{n} ) bigr} geq1 quadmbox{for all }ninmathbb{N} provided that ({x_{n}}subseteq X) is a sequence such that ({fx_{n}}rightarrow gu) and (alpha ( x_{n},x_{n+1} ) geq1) for all (ninmathbb{N}).

Given two self-mappings (T,g Xrightarrow X), we will say that a point (xin X) is a coincidence point of T and g if (Tx=gx).

Although any deterministic mappings might be equally useful, we will focus our discussion on a class of algorithms that obtain implicit mappings by minimization of a cost function that includes measures of data mismatch and model variable mismatch.