Sentence examples for utilizing the convexity of from inspiring English sources

Utilizing the convexity of, we get from (H1) (2.20).

In this section, we first utilize the convexity of the function.

In this section, we firstly utilize the convexity of the function g ( u ) to obtain a unitarily invariant norms inequality that leads to another version of the inequality (1.6), which is also the refinement of the inequality (1.5).

As an alternative, an iterative algorithm has been developed by utilizing the convexity property of the cost function w.r.t. a part of the whole power coefficients.

Utilizing the technique of the modulus of convexity and a new demiclosed principle for nonself-maps of Kazor [24], we establish the weak convergence theorem of the three-step iterative scheme in a uniformly convex Banach space that satisfies Opial's condition or whose dual space has the Kadec-Klee property, which extends and improves the recently announced ones in [4, 16, 18 20].

And to be sure, our expectations concerning the convexity of faces seem especially strong and potent.

The convexity of F ( T ) is proved.

(iii) follows from the convexity of ϱ. □.

A contradiction to the convexity of follows.

Let us establish the convexity of Λ.

Then, by the convexity of, (2.6).