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Paper   IPM / M / 16895
School of Mathematics
Title:   Fixed points of nearly quasi-closed and nearly almost convex mappings
Author(s):
 1 Alireza Amini-Harandi 2 Hamidreza Hajisharifi (Joint with M. Fakhar)
Status:   Published
Journal: J. Math. Anal. Appl.
Vol.:  502
Year:  2021
Pages:   125236
Supported by:  IPM
Abstract:
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].