Retkes identities

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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.

Particular cases[edit]

Since is strictly convex if , strictly concave if , linear if , the following inequalities and identities hold:

Consequences[edit]

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:

References[edit]