Relative and mutual monotonicity - PINTEA, Cornel (Studia Universitatis Babeș-Bolyai Mathematica, 2022)
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 injective operators, we define what we call mutual h-monotonicity and prove that every two mutual h-monotone local diffeomorphisms can be obtained from each other via a composition with a h-monotone diffeomorphism. Mathematics Subject Classification (2010): 47H99, 55M25, 55M20. Received 15 December 2021; Accepted 29 December 2021.