Integral Representations for Bivariate Complex Geometric Mean and Applications

In the paper, the authors survey integral representations (including the Lévy--Khintchine representations) and applications of some bivariate means (including the logarithmic mean, the identric mean, Stolarsky's mean, the harmonic mean, the (weighted) geometric means and their reciprocals, and the Toader--Qi mean) and the multivariate (weighted) geometric means and their reciprocals, derive integral representations of bivariate complex geometric mean and its reciprocal, and apply these newly-derived integral representations to establish integral representations of Heronian mean of power 2 and its reciprocal.

On trapezoid inequality via Gruss type result and applications

In this paper, we point out a Gr"uss type inequality and apply it for special means (logarithmic mean, identric mean etc ...) and in Numerical analysis in connection with the classical trapezoid formula.

ON SIMPSON'S QUADRATURE FORMULA FOR MAPPINGS OF BOUNDED VARIATION AND APPLICATIONS

An estimation of remamder for Simpson's quadrature formula for mappings of bounded variation and applications in theory of special means (logarithmic mean, identric mean, etc ...) are given.