Sentence examples for be a mapping for from inspiring English sources

Set and let be a mapping for all by (3.34).

Let be a mapping for which there exists a function satisfying (2.2) such that (4.1).

Let be a mapping for which there exists a function satisfying (2.2), (2.3), and (2.4).

Let be a mapping for which there exists a function such that (2.2). (2.3).

Let be a mapping for which there exist functions such that (2.32).

Let be a mapping for which there exist functions and such that (3.2). (3.3).

Let be a map for which there exist real numbers satisfying.

Suppose that is a mapping for which there exists a function such that (2.25).

where the set function is a mapping for all subsets of to the positive real numbers.

Assume that is a mapping for which there exist constants and such that and satisfies the functional inequality (1.8).

Let be a mapping satisfying for which there is a function satisfying (2.6), (2.7) and (2.26).