In the mathematical analysis, there are some theorems and definitions that established for both real and fuzzy numbers. In this study, we try to prove  Bernoulli's inequality in fuzzy real numbers with some of its applications. Also, we prove two other theorems in fuzzy real numbers which are proved before, for real numbers.

There is only one pair of non-real zeros of ζ′′(s), and of ζ′′′(s), in the left half-plane. The Riemann Hypothesis implies that ζ′′(s) and ζ′′′(s) have no zeros in the strip 0 ≤ <s < 1 2 . It was shown by Speiser [3] that the Riemann Hypothesis is equivalent to ζ′(s) having no zeros in 0 < σ < 12 (as usual we write s = σ + it). Levinson and Montgomery [2] gave a different proof; moreover, they ...

Abstract Let f :=(f1, . . . , fn) be a sparse random polynomial system. This means that each f i has fixed support (list of possibly non-zero coefficients) and each coefficient has a Gaussian probability distribution of arbitrary variance. We express the expected number of roots of f inside a region U as the integral over U of a certain mixed volume form. When U = (C∗)n, the classical mixed vol...

For a positive semi-definite biquadratic forms F in (3, 3) variables, we prove that if F has a finite number but at least 7 real zeros Z(F ), then it is not a sum of squares. We show also that if F has at least 11 zeros, then it has infinitely many real zeros and it is a sum of squares. It can be seen as the counterpart for biquadratic forms as the results of Choi, Lam and Reznick for positive ...

First year undergraduates usually learn about classical Rolle’s theorem saying that between two consecutive zeros of a smooth univariate function f one can always find at least one zero of its derivative f . In this paper we study a generalization of Rolle’s theorem dealing with zeros of higher derivatives of smooth univariate functions enjoying a natural additional property. Namely, we call a ...

where l > 0 and {dk0, dk1} is a so-called symmetrically coherent pair, with dk0 or dk1 the classical Gegenbauer measure (x−1) dx, a > −1. If dk1 is the Gegenbauer measure, then Sn has n different, real zeros. If dk0 is the Gegenbauer measure, then Sn has at least n−2 different, real zeros. Under certain conditions Sn has complex zeros. Also the location of the zeros of Sn with respect to Gegenb...

Let [Formula: see text] be a real and non-principal Dirichlet character, its text]-function let generic prime number. We prove the following result: If for some partial sums change sign only finite number of integers text], then there exists such that has no zeros in half plane text].