Sentence examples for on distinct points from inspiring English sources

The rational contractive conditions of [1, 2] are applicable only on distinct points of the considered metric spaces.

The general rational contractive conditions of [1, 2] are applicable only on distinct points of the considered metric spaces.

Let be a sequence of distinct points on the unit circle, and let We now define a continuous fixed-point free map for which.

It is well known that an affine transform preserves the collinearity of points, and also the ratios of the distances of distinct points on a line.

(A4) Through each point X not on a line l, at least two lines pass not meeting (parallel to) l. (A5) If a subset S of the points contains all points on the lines through pairs of distinct points of S, then the subset S contains all points of the geometric structure (see [11 14]).

It aims to detect the range of distinct points of view, on any given topic within a given population, by requiring participants to consider and respond to a set of predefined attitudinal statements on the topic under investigation [ 20].

A function is said to be -convex on,, if and only if for all choices of distinct points in, (52).

What I had thought nebulous took on a distinct point of view.

These comparisons were based on metric measurements between distinct points on the femur, but not true three-dimensional (3D) analysis (Cheng et al. 2009; Ho et al. 2006).

(A2) Two distinct points lie on one and only one line.

Geometrically, this means that if, and are three distinct points on the graph of with between and, then is on or below chord.