In mathematics, the Retkes Identities, named after Zoltán Retkes, are one of the most efficient applications of the Retkes inequality, when , , and . In this special setting, one can have for the iterated integrals
The notation is explained at Hermite–Hadamard inequality.
One of the consequences of the case is the Retkes convergence criterion because of the right side of the equality is precisely the nth partial sum of
Assume henceforth that Under this condition substituting instead of in the second and fourth identities one can have two universal algebraic identities. These four identities are the so-called Retkes identities:
- Zoltán Retkes (2008). "An extension of the Hermite—Hadamard inequality". Acta Sci. Math. (Szeged) 74: 95–106.
- Zoltán Retkes (2006). "Applications of the extended Hermite—Hadamard inequality". Journal of Inequalities in Pure and Applied Mathematics (JIPAM) 7 (1): article 24.