Related papers: On the Minkowski-H\"{o}lder type inequalities for …
We prove a~general form of Chebyshev type inequality for generalized upper Sugeno integral in the form of necessary and sufficient condition. A key role in our considerations is played by the~class of $m$-positively dependent functions…
In this paper, we have proved Diaz-Metcolf inequality for fuzzy integrals.
We present a Carlson type inequality for the generalized Sugeno integral and a much wider class of functions than the comonotone functions. We also provide three Carlson type inequalities for the Choquet integral. Our inequalities…
We give solutions to Problems 2.21, 2.31 and 2.32, which were posed Borzow\'a-Moln\'arov\'a, Hal\v{c}inov\'a and Hutn\'ik in [{\it The smallest semicopula-based universal integrals I: properties and characterizations,} Fuzzy Sets and…
In this study, we obtain some new integral inequalities for different classes of convex functions by using some elementary inequalities and classical inequalities like general Cauchy inequality and Minkowski inequality.
In this paper, a new two-dimensional Hardy type inequality is given in terms of pseudo-analysis dealing with set-valued functions. The first one is given for a pseudo-integral of set-valued function where pseudo-addition and…
The purpose of this paper is to study the Hermite-Hadamard type inequality for r-preinvex and ({\alpha}, m)-preinvex function which is based on Sugeno integral.
We use the definition of a fractional integral, recently proposed by Katugampola, to establish a generalization of the reverse Minkowski's inequality. We show two new theorems associated with this inequality, as well as state and show other…
In this paper we present new versions of the classical Brunn-Minkowski inequality for different classes of measures and sets. We show that the inequality \[ \mu(\lambda A + (1-\lambda)B)^{1/n} \geq \lambda \mu(A)^{1/n} +…
We give a systematic and thorough study of geometric notions and results connected to Minkowski's measure of symmetry and the extension of the well-known Minkowski functional to arbitrary, not necessarily symmetric convex bodies K on any…
For a broad class of integral functionals defined on the space of $n$-dimensional convex bodies, we establish necessary and sufficient conditions for monotonicity, and necessary conditions for the validity of a Brunn-Minkowski type…
Elementary proofs of sharp isoperimetric inequalities on a normed space $(\mathbb{R}^n,||\cdot||)$ equipped with a measure $\mu = w(x) dx$ so that $w^p$ is homogeneous are provided, along with a characterization of the corresponding…
In this work, the $L_p$ version (for $p> 1$) of the dimensional Brunn-Minkowski inequality for the standard Gaussian measure $\gamma_n(\cdot)$ on $\mathbb{R}^n$ is shown. More precisely, we prove that for any $0$-symmetric convex sets with…
The purpose of this paper is to establish several necessary and sufficient conditions to ensure the validity of a general functional inequality in terms of generalized quasi-arithmetic means. In particular cases, we consider H\"older-,…
The mixed-norm versions of the H\"older and Minkowski integral inequalities are used to produce new, general estimates involving symmetric geometric means of mixed norms. Various existing mixed-norm estimates are shown to be simple special…
In this paper, we obtain new results related to Minkowski fractional integral inequality using generalized k-fractional integral operator which is in terms of the Gauss hypergeometric function.
We generalize the classical Minkowski integral inequality to the form involving general Banach function norms.
Some inequalities and reverses of classic H\"{o}lder and Minkowski types are obtained for scalar Birkhoff weak integrable functions with respect to a non-additive measure.
We obtain inequalities of H\"{o}lder and Minkowski type with weights generalizing both the case of weights with alternating signs and the classical case of non-negative weights.
A Sobolev type embedding for radially symmetric functions on the unit ball $B$ in $\mathbb R^n$, $n\geq 3$, into the variable exponent Lebesgue space $L_{2^\star + |x|^\alpha} (B)$, $2^\star = 2n/(n-2)$, $\alpha>0$, is known due to J.M. do…