Some Generalizations of Mercer inequality and its operator extensions

Mohsen Kian, Zainab Peymani Mazraj

Published 2024-03-26Version 1

We study the Mercer inequality and its operator extension for superquadratic functions. In particular, we give a more general form of the Mercer inequality by replacing some constants by positive operators. As some consequences, our results produce a Jensen operator inequality for superquadratic functions. Moreover, we present some Mercer inequalities of Hermite-Hadamard's type.