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    STUDIA MATHEMATICA - Issue no. 4 / 2012  
         
  Article:   ABOUT SOME LINKS BETWEEN THE DINI-HADAMARDLIKE NORMAL CONE AND THE CONTINGENT ONE.

Authors:  . 		 
       
         
  Abstract:  The primary goal of this paper is to furnish an alternative description for the contingent normal cone, similar to the one that exists for the Fréchet one, but by using a directional convergence in place of the usual one. In fact, we actually prove that the same description is available not only for the contingent normal cone, but also for the Dini-Hadamard normal cone and the Dini-Hadamard-like one. Furthermore, we show that although in the case of the Dini-Hadamard subdifferential the geometric construction agrees with the analytical one, in the case of the Dini-Hadamard - like one the analytical construction is only greater than the geometrical one.
Mathematics Subject Classification (2010): 46B20, 49J52, 90C56.

Keywords: Contingent normal cone, Dini-Hadamard and Dini-Hadamard-like subdifferentials, geometrical and analytical constructions, sponge, calm functions, directional derivatives. 		 
         
     
         
         
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