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    STUDIA MATHEMATICA - Issue no. 1 / 2022  
         
  Article:   CONTINUITY AND MAXIMAL QUASIMONOTONICITY OF NORMAL CONE OPERATORS.

Authors:  MONICA BIANCHI, NICOLAS HADJISAVVAS, RITA PINI.
 
       
         
  Abstract:  
DOI: 10.24193/subbmath.2022.1.03

Published Online: 2022-03-10
Published Print: 2022-03-31
pp. 31-45

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In this paper, we study some properties of the adjusted normal cone operator of quasiconvex functions. In particular, we introduce a new notion of maximal quasimotonicity for set-valued maps different from similar ones recently appeared in literature, and we show that it is enjoyed by this operator. Moreover, we prove the s x w* cone upper semicontinuity of the normal cone operator in the domain of f in case the set of global minima has non empty interior.

Keywords: Quasimonotone operator, maximal quasimonotone operator, cone upper semicontinuity, upper sign continuity, quasiconvex function.

Mathematics Subject Classification (2010): 47H05, 47H04, 49J53, 90C33.
 
         
     
         
         
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