Sentence examples for dominating functions in from inspiring English sources

Dominating functions in the molecular signature.

This leads to the counterparts of the explicit representation in Proposition 23 and to the dominating function in Corollary 24 by using the area formula (e.g., [35, § 3.3, Theorem 2]) rather than the change of variables formula for Lebesgue integrals.

It should be mentioned that in this paper we remove the lower semicontinuity property of the dominated functions in Caristi-type cyclic maps.

Furthermore, we also discuss the results with the lower semicontinuities of the dominated functions in place of the original orbital continuities of the mappings.

Based on this, we also assume the dominating function λ that in (1.1) satisfies (1.2) in this paper.

Based on this, in this paper, we always assume that the dominating function λ also satisfies it.

Remark 2 If function φ is the identity in (2.6) and (2.7), then they reduce to Hermite-Hadamard type inequalities for ( g, s ) -convex dominated functions proved by Kavurmacı, Özdemir and Sarıkaya in [4].

It should be mentioned that in our results, the dominated functions need not possess the lower semicontinuity property.

In [2], Dragomir et al. proved the following theorem for g-convex dominated functions related to (1.1).

The problem is that form (kata) dominates function and purpose (jitsu) in every nook and cranny of Japanese life.

In this paper, we introduce the notion of ( g, φ h ) -convex dominated function and present some properties of them.