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Paper IPM / M / 16895  


Abstract:  
In this paper, we ï¬rst obtain a characterization of transfer weakly lower continuous
functions. Then, by introducing the class of nearly quasiclosed setvalued mappings,
we obtain some characterizations of setvalued mappings whose displacement
functions are transfer weakly lower continuous. We also present some ï¬xed point
theorems for nearly quasiclosed setvalued mappings which are either nearly almost
convex or almost aï¬ne. Finally, we construct an almost aï¬ne mapping T :[0, 1) â
R,
which is not Î±almost convex for any continuous and strictly increasing function
Î± :[0, +â) â [0, +â)with Î±(0) =0. This example gives an aï¬rmative response
to the Question 3 of Jachymski (2015) [8].
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