Sentence examples for partial spaces from inspiring English sources

A lot of fixed point theorems were investigated in partial spaces (see, e.g., [3 11] and references therein).

The comma before an index represents partial space differentiation and dot over a variable represents partial time derivative.

Every quasi-partial space is a quasi-partial b-metric space.

In partial metric spaces, the distance of a point in the self may not be zero.

More recently, Kulpa and Szymanski [38] found some partial KKM spaces which are not KKM spaces.

Let ( X, d ) and ( X, p ) be metric space and partial metric space, respectively.

The concepts of b-metric space and partial metric space were introduced by Czerwik [1] and Matthews [2], respectively.

In 1994, Matthews [1] introduced the notion of partial metric spaces and extended the Banach contraction principle from metric spaces to partial metric spaces.

Later on, many researchers studied fixed point theorems in partial metric spaces as well as ordered partial metric spaces.

First, we prove such a type of fixed point theorem in compact partial metric spaces, and then generalize to complete partial metric spaces.

Matthews [16] introduced the notion of partial metric spaces, and extended Banach's contraction principle to partial metric spaces, and then a lot of authors gave fixed point results in partial metric spaces (see [5, 17 30]).