A number of integral inequalities of Hölder and Minkowski type involving a class of generalized weighted quasi-arithmetic means in integral form is established. Some well known inequalities and their generalizations are derived as consequences of our results.
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...
Page 1