On a certain condition of the monotonicity of functions
We solve Matkowski's problem for strictly comparable quasi-arithmetic means.
We define absolutely monotone multifunctions and prove their analyticity on an interval [0,b).
We give a positive answer to two open problems stated by Boczek and Kaluszka in their paper [1]. The first one deals with an algebraic characterization of comonotonicity. We show that the class of binary operations solving this problem contains any strictly monotone right-continuous operation. More precisely, the comonotonicity of functions is equivalent not only to -associatedness of functions (as proved by Boczek and Kaluszka), but also to their -associatedness with being an arbitrary strictly...