On the associativity functional equation
The author describes the class of continuous, nondecreasing, associative functions \(M:[a,b]^2 \to[a,b]\) such that \(M(a,a)=a\) and \(M(b,b)=b\), where \([a,b]\) is a bounded closed real interval. To this end the author surveys many known results of J. Aczél, C. H. Ling, B. Schweizer, A. Sklar, J. C. Fodor, E. Czogala, J. Drewniak, P. S. Mostert and A. L. Shields. A new result is presented dealing with the class \(A_{a,b}\) of continuous, nondecreasing, associative functions \(M\) such that \(M(a,a)=a\) and \(M(b,b)=b\) and the subclass \(A_{a,b,c}\) where \(M(a,b)= M(b,a)=c\), \(c\in[a,b]\).
scientific article; zbMATH DE number 1517317