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In this paper, we ï¬rst obtain a characterization of transfer weakly lower continuous
functions. Then, by introducing the class of nearly quasi-closed set-valued mappings,
we obtain some characterizations of set-valued mappings whose displacement
functions are transfer weakly lower continuous. We also present some ï¬xed point
theorems for nearly quasi-closed set-valued 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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