New reverses of the Schwarz inequality in inner product spaces that incorporate the classical Klamkin-McLenaghan result for the case of positive n−tuples are given. Applications for Lebesgue integrals are also provided.

In this paper, some estimates of third and fourth inequalities in Hermite–Hadamard-type for coordinated convex functions are proved using the non-additivity integrals Fubini’s theorem fuzzy integrals. That is, results obtained context Lebesgue measure. Several examples provided on how to evaluate these order illustrate results.

A companion of the Grüss inequality in the general setting of measurable spaces and abstract Lebesgue integrals is proven. Some particular inequalities are mentioned as well. An application for the moments of guessing mapping is also provided.

This short note gives an introduction to the Riemann-Stieltjes integral on R and Rn. Some natural and important applications in probability theory are discussed. The reason for discussing the Riemann-Stieltjes integral instead of the more general Lebesgue and LebesgueStieltjes integrals are that most applications in elementary probability theory are satisfactorily covered by the Riemann-Stieltj...

We derive sharp partial regularity criteria of nonlinear potential theoretic nature for the Lebesgue-Serrin-Marcellini extension nonhomogeneous singular multiple integrals featuring (p,q)-growth conditions.

The paper presents a new fractional integration, which generalizes the Riemann-Liouville and Hadamard fractional integrals into a single form, which when a parameter fixed at different values, produces the above integrals as special cases. Conditions are given for such a generalized fractional integration operator to be bounded in an extended Lebesgue measurable space. Semigroup property for th...