Relative and mutual monotonicity

"In this work we first consider a certain monotonicity relative to some given one-to-one operator and prove the counterparts, adjusted to this new con- text, of most results obtained before in the joint work with G. Kassay [10]. For two operators with the same status relative to injectivity, such as two local in- jective operators, we de ne what we call mutual h-monotonicity and prove that every two mutual h-monotone local di eomorphisms can be obtained from each other via a composition with a h-monotone diffeomorphism."