Relative and mutual monotonicity
DOI:
https://doi.org/10.24193/subbmath.2022.1.05Keywords:
Minty-Browwder monotonicity, $h$-monotonicity, mutual $h$-monotonicityAbstract
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 context, of most results obtained before in the joint work with G. Kassay \cite{Kassay-Pintea}.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.
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2022-03-10
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