Analysis of α-fractal functions without boundary point conditions on the Sierpiński gasket

This note aims to manifest the existence of a class of α-fractal interpolation functions (α-FIFs) without boundary point conditions at the m-th level in the space consisting of continuous functions on the Sierpiński gasket (SG). Furthermore, we add the existence of the same class in the Lp space and energy space on SG. Under certain hypotheses, we show the existence of α-FIFs without boundary point conditions in the Hölder space and oscillation space on SG, and also calculate the fractal dimensions of their graphs. © 2024 Elsevier Inc.