Sentence examples for a partially order from inspiring English sources

Suppose that S has a partially order relation ≤.

Also, in these years many authors have focused on different contractive conditions in complete metric spaces with a partially order and have obtained some common fixed point theorems.

A metric space (X, d) together with a partially order "(preceq)" on it is called ordered metric space and denoted by ((X,d,preceq )).

Suppose we have a finite set Y and a partially order (finite or infinite) set W, together with some functions f:2 Y → W and g: Y→ W. Consider the fixed points of the map ψ:2 Y →2 Y where ψ(A):={ y∈ A: g y)≤ f(A)}, other than ∅.

We say that a Banach space endowed with a partial order is a partially ordered Banach space if it is both a partially ordered vector space and a partially ordered topological space with respect to the norm topology.

A set with a partial order ⪯ is called a partially ordered set.

A set together with a definite partial ordering is called a partially ordered set.

Throughout this article, (X, ≼) denotes a partially ordered set with the partial order ≼.

Throughout this paper, ( X, ≤ ) denotes a partially ordered set with the partial order ≤.

Let ⪰ be a partial order on B satisfying that ( B, ⪰ ) is a partially ordered vector space.

A partially ordered topological vector space is both a partially ordered topological space and a partially ordered vector space.