Multivariate Fractal Functions in Some Complete Function Spaces and Fractional Integral of Continuous Fractal Functions

There has been a considerable evolution of the theory fractal interpolation function (FIF) over last three decades. Recently, we introduced multivariate analogue special class FIFs, which is referred to as α-fractal functions, from viewpoint approximation theory. In current note, continue our study on but in context few complete spaces. For functions defined hyperrectangle Ω Euclidean space Rn, derive conditions defining parameters so that are elements some standard spaces such Lebesgue Lp(Ω), Sobolev Wm,p(Ω), and Hölder Cm,σ(Ω), Banach As simple consequence, for choices parameters, provide bounds Hausdorff dimension graph corresponding function. We shall also hint at an associated notion operator maps each one these its counterpart. The latter part this note establishes Riemann–Liouville fractional integral continuous similar kind.