Sentence examples for proved the mean value from inspiring English sources

In this manuscript, we have proved the mean value theorem and Taylor's theorem for derivatives defined in terms of a Mittag Leffler kernel.

In Section 2, we give the generalization of Mitrinović-Pečarić inequality and prove the mean value theorems of Cauchy type.

We prove that the mean value operator over translated K-orbits of a fixed point is surjective on the space of smooth functions on X if X is either complex or of rank one.

SL A and Sagm A have a similar distribution, and the corresponding P-value proves that the mean values are not significantly different (see Fig.  4E).

We discuss the relationship between the notion of column spacing and the structure of correlation spectra; we prove formulas for the mean value and variance of column spacing, and we use numerical analysis of exact analytic formulae to study the variance.

Specifically, our aim is to prove generalised versions of the mean value theorem and Taylor's theorem in the AB model of fractional calculus.

We can use this fact to prove the following analogue of the mean value theorem for fractional derivatives in the AB model.

We will use the following lemma [11] to prove the related mean value theorems of Cauchy type.

It is not difficult to prove it as a consequence of the Mean Value Theorem and the following interpolation property satisfied by the sequence of projections (see [1]): whenever and then (2.9).

Willet and Wong [12, Theorem  4] proved the nonlinear difference inequality by using the mean value theorem.

mean The mean value of the array.