July 2020
Intermediate to advanced
384 pages
11h 25m
English
Classical approximation theory of real‐valued continuous functions by algebraic or trigonometric polynomials has been a subject of research for more than two centuries (see, e.g. [72, 164, 194, 286] for a rigorous as well as instructive presentation). Here, we are going to give a brief account of some basic results of approximation theory put in a fuzzy setting.
Let us recall two of the most fundamental questions in classical approximation theory:
Both questions, that are actually intrinsically interrelated, were answered affirmatively by Karl Theodor Wilhelm Weierstrass in 1885 through perhaps the most significant result in approximation theory known as Weierstrass approximation theorem which, in its basic form, reads: