Sentence examples for proved that the function from inspiring English sources

Later McIntosh [45] and Kato [35] proved that the function (xmapsto |x|) is not operator Lischitz.

Recently, in [6], Qi and Sun proved that the function (1.6). is strictly increasing with respect to for all.

In fact, they proved that the function is a solution of (1.1) if and only if where the function is symmetric and additive in each variable.

This work is motivated by an paper of Guo [46], who proved that the function (1.7). is strictly logarithmically concave and strictly increasing from onto.

Hence, we have proved that the function (phi (x)) is nonincreasing on (mathbb{T}_{0}) (see Definition 2.4) so the proof is complete.

Remark 3.2 Very recently, Karapınar and Samet [15] proved that the function d φ = φ ∘ d on the set X, where φ ∈ Ψ is also a metric on X.

In [1], the author proved that the functions G α and g α are pointwise comparable.

In [17], the author proved that the functions G α f and g α f are pointwise comparable.

We first prove that the function, defined by, satisfies the inhomogeneous Kummer's equation (1.4).

Indeed, we prove that the function H has a global minimum at x = b.

In this section we prove that the function in Equation 10 has a fixed point.