Solving an abstract nonlinear eigenvalue problem by the inverse iteration method

Let $(X,{\parallel \cdot \parallel }_X)$ and $\left( Y,\left\Vert \cdot\right\Vert_{Y}\right) $beBanachspacesover$$\mathbb{R}$,$with$X$uniformlyconvexandcompactlyembeddedinto$Y.$ The inverse iteration method is applied to solve the abstract eigenvalue problem $A(w)=\lambda {\parallel w\parallel }_Y^{p-q}B(w),$ where the maps $A:X\to X^{\star }$ and $B:Y\to Y^{\star }$ are homogeneous of degrees $p-1$ and $q-1,$ respectively.