MathDB
Continuous function being monotone

Source: Miklós Schweitzer 2010, P6

September 9, 2020
continuous functionfunction

Problem Statement

Is there a continuous function f:R2→R f: \mathbb {R} ^ {2} \rightarrow \mathbb {R} for every d∈R d \in \mathbb {R} we have gm,d(x)=f(x,mx+d) g_{m,d}(x) = f (x, m x + d) is strictly monotonic on R \mathbb {R} if m≥0, m \ge 0, and not monotone on any non-empty open interval if m<0? m <0?
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