ON BIVARIATE FRACTAL INTERPOLATION FOR COUNTABLE DATA AND ASSOCIATED NONLINEAR FRACTAL OPERATOR

The paper’s main theorem (existence/uniqueness of a continuous CFIF g interpolating a countable grid and whose graph is the attractor) is proved by defining a contraction T on a corner-anchored function space C*(I×J) using the α-contractivity in z and matching conditions (3.13)–(3.14), then identifying G=graph(g) as the unique W-invariant set, i.e., the CFIS attractor . The model’s solution establishes the same result via a different route: it equips X with a weighted max-metric to make all Wij contractions and then shows the attractor is a graph by vertical fiber shrinkage driven by α<1. This alternative proof is sound and standard. A minor issue in the paper is the choice of δ in Proposition 3.1 (δ := inf(1−2δij)/(2θ)), which can be nonpositive if some δij>1/2; it suffices to choose any 0<δ<(1−sup δij)/θ to ensure hyperbolicity of the CIFS . This does not affect the main theorem’s correctness, which does not rely on that specific δ value.