Simple Fixed Point Theorems on Linear Continua
A simple fixed point theorem is formulated for multivalued maps with a connected graph on closed intervals of linear continua. These intervals either cover themselves or are concerned with self-maps. We discuss a question when the original map can possess a fixed point, provided the same assumptions are satisfied only for some of its iterate. We are particularly interested in a situation on noncompact connected linearly ordered spaces. Many illustrating examples are supplied.