Peierls–Bogolyubov’s Inequality for Deformed Exponentials - Frank Hansen; Jin Liang; Guanghua Shi (Entropy, 2017)
We study the convexity or concavity of certain trace functions for the deformed logarithmic and exponential functions, and in this way obtain new trace inequalities for deformed exponentials that may be considered as generalizations of Peierls–Bogolyubov’s inequality. We use these results to improve previously-known lower bounds for the Tsallis relative entropy.