Keywords: Fuzzy measure Sugeno integral Choquet integral Stolarsky's inequality a b s t r a c t Recently Flores-Franulič, Román-Flores and Chalco-Cano proved the Stolarsky type inequality for Sugeno integral with respect to the Lebesgue measure k. The present paper is devoted to generalize this result by relaxing some of its requirements. Moreover, Stolar-sky inequality for Choquet integral is ...

In this work, we obtain quantitative convergence of moderately interacting particle systems towards solutions nonlinear Fokker-Planck equations with singular kernels. addition, prove the well-posedness for McKean-Vlasov SDEs involving these kernels and trajectorial propagation chaos associated systems. Our results only require very weak regularity on interaction kernel, including Biot-Savart at...

It has recently been shown that the Lebesgue constant for Berrut’s rational interpolant at equidistant nodes grows logarithmically in the number of interpolation nodes. In this paper we show that the same holds for a very general class of well-spaced nodes and essentially any distribution of nodes that satisfy a certain regularity condition, including Chebyshev–Gauss–Lobatto nodes as well as ex...

Abstract In this note, it is proved the existence of a $$\mathfrak {c}$$ c -dimensional vector space real-entire functions all whose nonzero members are non-integrable in sense Lebesgue but yet their two iterated integrals exist as real numbers and coincide. Moreover, shown that can be chosen to dense $$C^\in...

Random or stochastic integral equations are important in the study of many physical phenomena in life sciences, engineering, and technology 1–13 . Currently there are two basic versions of stochastic integral equations being studied bymathematical statisticians and probabilists namely, those integral equations involving Ito-Doob type of stochastic integrals and those which can be formed as prob...

We consider autonomous integrals F [u] := ∫ Ω f (Du)dx for u : R ⊃ Ω →R in the multidimensional calculus of variations, where the integrand f is a strictly quasiconvex C2-function satisfying the (p,q)-growth conditions γ|A| ≤ f (A)≤ Γ (1+ |A|) for every A ∈R with exponents 1 < p ≤ q < ∞. We examine the Lebesgue-Serrin extension Floc[u] := inf { liminf k→∞ F[uk] : W 1,q loc ∋ uk −−−⇀ k→∞ u weakl...

1971 The purpose of this paper is to exhibit a theory of integration which can be used on a large class of topological spaces and which generalizes the theory of integration over the locally compact Hausdorff spaces. The first part of the paper is devoted to the construction of such a theory. An integral is viewed as a positive linear functional having a certain extension property on a particul...

1. A. Aksoy and M. Martelli, Mixed partial derivatives and Fubini’s theorem, College Math. J. 33 (2002) 126–130. 2. D. D. Ang, K. Schmitt, and L. K. Vy, A multidimensional analogue of the Denjoy-Perron-HenstockKurzweil integral, Bull. Belg. Math. Soc. Simon Stevin 4 (1997) 355–371. 3. M. W. Botsko, An elementary proof that a bounded a.e. continuous function is Riemann integrable, this MONTHLY 6...

We study the complexity of approximating stochastic integrals with error ε for various classes of functions. For Ito integration, we show that the complexity is of order ε−1, even for classes of very smooth functions. The lower bound is obtained by showing that Ito integration is not easier than Lebesgue integration in the average case setting with the Wiener measure. The upper bound is obtaine...

SECTION 1 introduces a method for constructing a measure by inner approximation, starting from a set function defined on a lattice of sets. SECTION 2 defines a “tightness” property, which ensures that a set function has an extension to a finitely additive measure on a field determined by the class of approximating sets. SECTION 3 defines a “sigma-smoothness” property, which ensures that a tight...