Existence of a class of vector-valued and multivariate α-fractal functions on a hype-rectangle of R^q

Key Points

• This research aims to explore the existence of multivariate α-fractal functions and their approximation properties in a high-dimensional setting.
• Proving existence of vector-valued multivariate α-fractal functions on a hype-rectangle in $ ext{R}^{q}$.
• Establishing density of these functions in continuous function space with respect to the uniform norm.
• Studying dimension-preserving approximation in the context of α-fractal functions.
• Investigating constrained approximation aspects based on dimension-preserving concepts.
• A class of vector-valued and multivariate α-fractal functions exists on the defined hype-rectangle.
• The set of these functions is dense in the continuous function space concerning the uniform norm.
• Dimension-preserving approximation properties are shown to hold in this general framework.
• Several approximation theoretic results, including the Weierstrass approximation theorem, are confirmed for these functions.