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    STUDIA MATHEMATICA - Issue no. 1 / 2022  
         
  Article:   RELATIVE AND MUTUAL MONOTONICITY.

Authors:  CORNEL PINTEA.
 
       
         
  Abstract:  
DOI: 10.24193/subbmath.2022.1.05

Published Online: 2022-03-10
Published Print: 2022-03-31
pp. 55-72

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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 [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.

Keywords: Minty-Browder monotonicity, h-monotonicity, mutual h-monotonicity.

Mathematics Subject Classification (2010): 47H99, 55M25, 55M20.
 
         
     
         
         
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