arXiv subjects

Juan J. Font

Publications and source records attributed to Juan J. Font.

5 recordsLinked to original sources

arXiv2025

Best approximation results for fuzzy-number-valued continuous functions

In this paper we study the best approximation of a fixed fuzzy-number-valued continuous function to a subset of fuzzy-number-valued continuous functions. We also introduce a method to measure the distance between a fuzzy-number-valued continuous function and a real-valued one. Then we prove the existence of the best approximation of a fuzzy-number-valued continuous function to the space of real-valued continuous functions by using the well-known Michael Selection Theorem.

math.GM↗

arXiv2025

Neural Network Operators on fuzzy number valued continuous functions

We extend Cardaliaguet-Euvrard neural network operators to the context of fuzzy number valued continuous functions and study their behaviour. We focus on level continuous, sendograph continuous and endograph continuous functions and obtain Jackson-type results in all these cases.

math.GM↗

arXiv2025

Jackson-type approximation for fuzzy-valued functions by means of trapezoidal functions

In this paper we provide new several Jackson-type approximations results for continuous fuzzy-number-valued functions which improve several previous ones. We use alternative techniques adapted from Interval Analysis which rely on the gH-difference (which might not exist) and the generalized difference (which might lack the cancellation law ) of fuzzy numbers.

math.GM↗

arXiv2008

Stability and instability of weighted composition operators

Let $ε>0$. A continuous linear operator $T:C(X) \ra C(Y)$ is said to be {\em $ε$-disjointness preserving} if $\vc (Tf)(Tg)\vd_{\infty} \le ε$, whenever $f,g\in C(X)$ satisfy $\vc f\vd_{\infty} =\vc g\vd_{\infty} =1$ and $fg\equiv 0$. In this paper we address basically two main questions: 1.- How close there must be a weighted composition operator to a given $ε$-disjointness preserving operator? 2.- How far can the set of weighted composition operators be from a given $ε$-disjointness preserving operator? We address these two questions distinguishing among three cases: $X$ infinite, $X$ finite, and $Y$ a singleton ($ε$-disjointness preserving functionals). We provide sharp stability and instability bounds for the three cases.

math.FA↗

arXiv2001

Isometric shifts and metric spaces

Let M be a complete metric space. It is proved that if the space or scalar-valued bounded continuous functions on M admits an isometric shift, then M is separable.

math.FA↗