We establish the Brunn-Minkowski-type inequality for Lp-dual mixed volumes of star duality of mixed intersection bodies.

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In this paper, we prove  Bellman type inequality for Sugeno integral and generalize it for pseudo-integrals. Furthermore, we generalize the Bellman's inequality in abstract spaces. The strengthened version of this inequality is demonstrated in pseudo-integrals and abstract spaces. Also, we illustrate theorems with some examples.

In this paper, we investigate  Godunova type inequality for Sugeno integrals in two cases. At the first case, we suppose that the inner integral is the  Riemann integral and the remaining two integrals are of Sugeno type. At the second case, all the integrals are assumed Sugeno integrals. We present several examples to illustrate  validity of our results.

In this paper, by using the Euler-Maclaurin expansion for the Riemann-,function, we establish an inequality of a weight coe, cient. Using this inequality, we derive a new reverse Hilbert's type inequality. As an applications, an equivalent form is obtained.

We extend the definition of boundary expansion to CW complexes and prove a Cheeger-Buser-type relation between the spectral gap of the Laplacian and the boundary expansion of an orientable CW complex.

In this paper, we have proved Diaz-Metcalf inequality for fuzzy integrals. More precisely:\\If $f, g: [0, 1]\to\mathbb{R}$ are continuous and strictly increasing functions, then the fuzzy integral inequality$$ - \hspace{-1em} \int_0^1 f^s d\mu\cdot  - \hspace{-1em} \int_0^1  g^sd\mu\le  - \hspace{-1em} \int_0^1\left(f\cdot g\right)^sd\mu,$$holds, where $s>1$ and $\mu$ is  the Lebesgue measure on $\mathbb{R}$. In addition, we have shown this inequality for pseudo-integrals.

In this paper, we have proved and stated the Sitaru-Schweitzer type inequality for fuzzy integrals and  also we state this inequality for pseudo-integrals in two classes. The first one is for  pseudo-integrals where pseudo-addition and pseudo-multiplication are constructed by a monotone continuous function $g:[0, \infty ]\to[0, \infty]$. Another one is given by the semiring $([a, b], \max, \odot)$ where an increasing function generates pseudo-multiplication.