Sentence examples for exists a function with from inspiring English sources

We have thus proved that the mapping satisfies the assumptions of Schauder's fixed point theorem and hence there exists a function with The proof of existence of a solution of (1.1) is complete.

In other words, there exists a function with as such that (2.3).

Since is a weakly Kannan map, there exists a function with for all, satisfying (2.1) for all.

By a solution of problem (1.10), (7), (8) we mean a function such that there exists a function with for each and (1.3), (1.4), (1.5) hold.

Next we show that there exists a positive number such that where Clearly is a bounded closed convex set in for each positive constant If it is not true, then for each positive number, there exists a function with and.

From [1] or [3] a E-J generalized Hausdorff matrix (for ) is regular if and only if there exists a function with such that (12). in which case is called the moment generating function, or mass function, for and is called moment sequence.

there exists a function v with absolutely continuous and essentially bounded derivative v ′ and essentially bounded derivative v ″ such that v ( t ) > 0, v ′ ( t ) ≤ 0, ( M v ) ( t ) ≤ 0, t ∈ [ 0, + ∞ ) ; (5.4).

Let f ( z ) be a transcendental meromorphic function with finite order σ, then there exists a function λ ( r ) with the following properties: (i) λ ( r ) is a non-negative and continuous function for r ≥ 0 with lim r ⟶ ∞ λ ( r ) = σ.

Further, there exists a function such that with on where (3.1).

If there exists a function, continuous on with at most the first order discontinuity at the point satisfying, and the inequality (2.7) on, the initial function (3.1).

The function is said to be subordinate to, or is said to be superordinate to, if there exists a function analytic in, with and such that.