A Finite Data Based Regularization in a Normed Linear Space Setting

One of the basic problems in mathematical learning theory is to identify a function $f: Ω\to {\mathbb R}$ with certain specific properties which fits a given training data $\{(x_i, ξ_i)\in Ω\times {\mathbb R}: i=1, \ldots, n\}$, in the sense that, $f(x_i) = ξ_i$ for $i=1, \ldots, n$, where $Ω$ is a