Sentence examples for be a nonempty positive from inspiring English sources

The only substantive requirement introduced by (5) is that there be a nonempty positive analogy.

Let X be a nonempty set, m a positive integer, and T: X → X a mapping.

Let X be a nonempty set, m a positive integer and T : X → X an operator.

Definition 3 [13] Let X be a nonempty set, m a positive integer and f : X → X an operator.

Definition 3.2 Let Y be a nonempty set, m a positive integer and T : Y → Y an operator.

Corollary 4.9 Let ( S, d X ) be a nonempty subset of the positive cone of a Riesz space ( X, ≽ X ), which contains 0. Suppose a set-valued mapping F : S → 2 S ∖ satisfies the following conditions: 1. F is ordered increasing upward on S;   2.

Let X be a nonempty set, r be a positive integer and f : X → X be a mapping.

Let X be a nonempty set, m be a positive integer and f : X → X an operator.

Let X be a nonempty set, k be a positive integer, f : X k → X and g : X → X be mappings.

Let X be a nonempty set, k be a positive integer and (f:X^{k}rightarrow X), (g:Xrightarrow X) be two weakly compatible mappings.

Definition 1.3 Let X be a nonempty set, k be a positive integer and f : X k → X be a mapping.