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Paper   IPM / M / 16895
School of Mathematics
  Title:   Fixed points of nearly quasi-closed and nearly almost convex mappings
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
In this paper, we first 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 fixed point theorems for nearly quasi-closed set-valued mappings which are either nearly almost convex or almost affine. Finally, we construct an almost affine mapping T :[0, 1) → R, which is not α-almost convex for any continuous and strictly increasing function α :[0, +∞) → [0, +∞)with α(0) =0. This example gives an affirmative response to the Question 3 of Jachymski (2015) [8].

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