  In this article the operator trace function $ \Lambda_{r,s}(A)[K, M] :=
{\operatorname{tr}}(K^*A^r M A^r K)^s$ is introduced and its convexity and
concavity properties are investigated. This function has a direct connection to
several well-studied operator trace functions that appear in quantum
information theory, in particular when studying data processing inequalities of
various relative entropies. In the paper the interplay between $\Lambda_ {r,s}$
and the well-known operator functions $\Gamma_{p,s}$ and $\Psi_{p,q,s}$ is used
to study the stability of their convexity (concavity) properties. This
interplay may be used to ensure that $\Lambda_{r,s}$ is convex (concave) in
certain parameter ranges when $M=I$ or $K=I.$ However, our main result shows
that convexity (concavity) is surprisingly lost when perturbing those matrices
even a little. To complement the main theorem, the convexity (concavity) domain
of $\Lambda$ itself is examined. The final result states that $\Lambda_{r,s}$
is never concave and it is convex if and only if $r=1$ and $s\geq 1/2.$
