\(A(\infty)\)-simultaneous rational approximation (Q1975272)

The problem of \(A(\infty)\) approximation is to approximate simultaneously two given continuous functions on the interval \([a,b]\) by one rational function with given degree structure and which has a positive denominator in \([a,b]\). This gives an approximation error for each of the two functions and the approximation criterion is to minimize the maximum of the two sup-norms of these errors. This paper proves existence and uniqueness of these approximants and gives a characterization of the \(A(\infty)\) approximant by a kind of equioscillation condition.