Abstract
Approximation theory encompasses a vast area of mathematics. The current context is primarily concerned with the concept of dimension preserving approximation for real-valued multivariate continuous functions defined on a domain . This chapter establishes quite a few results similar to well-known results of multivariate constrained approximation in terms of dimension preserving approximants. In particular, this chapter gives indication for construction of multivariate dimension preserving approximants using the concept of fractal interpolation functions. In the last part, some multi-valued fractal operators associated with multivariate -fractal functions are defined and studied.
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