Fixed points of nearly quasi-closed and nearly almost convex mappings

Abstract

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]. © 2021 Elsevier Inc.