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In this paper, we introduce two notions of a relative operator $(\alpha,\beta)$-entropy and a Tsallis relative operator $(\alpha, \beta)$-entropy astwo parameter extensions of the relative operator entropy and the Tsallisrelative operator entropy. We apply a perspective approach to prove the jointconvexity or concavity of these new notions, under certain conditionsconcerning $\alpha$ and $\beta$. Indeed, we give the parametric extensions, butin such a manner that they remain jointly convex or jointly concave.

Convexity of parameter extensions of some relative operator entropies with a perspective approach