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.

The norm of a Hilbert’s type linear operator T: L2 (0, ¥)®L2 (0, ¥) is given. By introducing some parameters, we give the norms of two extensions of Hilbert’s Integral operator. Also, we obtain two new extended Hilbert’s type inequalities with constant factors and the equivalent forms are obtained.

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In this paper, we  present a version of Favard's inequality for special case and then generalize it for the Sugeno Integral in fuzzy measure space $(X,\Sigma,\mu)$, where $\mu$ is the Lebesgue measure. We consider two cases, when our function is concave and when is convex. In addition for illustration of theorems, several examples are given.

The classical Bohr inequality says that |a+b|2 £ p½a½2+q½b½2 for all scalars a, b and p, q > 0 with 1/p + 1/q = 1. The equality holds if and only if (p-1)a = b. Several authors discussed operator version of Bohr inequality. In this paper, we give a unified proof to operator generalizations of Bohr inequality. One viewpoint of ours is a matrix inequality, and the other is a generalized parallelogram law for absolute value of operators, i.e., for operators A and B on a Hilbert space and t¹0, ½A-B½2+ 1/t½T A+B½2= (1+t) A½2 +(1+1/t) B½2.

In this paper, we express and prove Chebyshev weighted type inequality for fuzzy Integrals and in abstract spaces where the functions are strictly monotone functions. Furthermore, we have shown our results for n-th strictly monotone functions. The theorems are illustrated with several examples.