Fixed point theory for maps having convexly totally bounded ranges (Q2770331)

The authors prove fixed point and continuation theorems for multi-valued maps using the concept of so-called convexly totally bounded sets. This extends and builds on previous work of \textit{A. Idzik} [Proc. Am. Math. Soc. 104, No. 3, 779-784 (1988; Zbl 0691.47046)] and \textit{A. Idzik} and \textit{S. Park} [Lect. Notes Nonlinear Anal. 2, 191-197 (1998)]. It seems that the authors are unaware of recent contributions of \textit{E. De Pascale}, \textit{G. Trombetta} and \textit{H. Weber} [Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 20, No. 3, 341-355 (1993; Zbl 0805.47055)] and \textit{G. Trombetta} [Bull. Pol. Acad. Sci., Math. 49, No. 3, 223-228 (2001; Zbl 1015.46003)] to this field.