Sentence examples for monotone functions by from inspiring English sources

In this paper, we give refinements of some inequalities for generalized monotone functions by using log-convexity of some functionals.

Since f is a continuously differentiable monotone function, by noticing Lemma 4.1, we can take a subsequence if necessary, without loss of generality denoted by {x k }, and an index i0 ∈ {1,..., r} such that either and is bounded below; or and is bounded above.

The theory of operator means for positive linear operators on a Hilbert space which in connection with Löwner's theory for operator monotone functions was established by Kubo and Ando [8].

We are interested in means of real-valued measurable functions induced by strictly monotone functions.

Moreover, by constructing one-parameter families of operator monotone functions, we will get many operator inequalities; especially, we will extend the Furuta inequality and the exponential inequality of Ando.

- Monotone functions, monotone circuit complexity.

Optimizing Monotone Functions Can Be Difficult.

The general activation functions include monotone nondecreasing functions, globally Lipschitz continuous and monotone nondecreasing functions, semi-Lipschitz continuous mixed monotone functions, and Lipschitz continuous functions.