Let $X=(X,|\cdot|)$ be a Banach space and let $\Gamma_1,\Gamma_2:B_r[0,X] \longrightarrow X$ such that $\Gamma_1$ is completely continuous and $\Gamma_2$ is a contraction. Under these conditions, $\Gamma_1+\Gamma_2$ is a condensing map?
Where, $B_r[0,X]$ denote de closed ball, of radius $r>0$, center $0 \in X$, in $X$.
That's true? I conjectured this, however I can not prove nor give a counterexample.