Abstract: 
It is proved that the cylinder $X\times I$ over a planar
$\lambda $-dendroid $X$ has the fixed point property. This is a
partial solution of two problems posed by R. H. Bing (cf. [1],
Questions 9 and 10).

1. Institute of Mathematics
   Polish Academy of Sciences
   Śniadeckich 8
   00-950 Warszawa, Poland