Abstract
Let f : X →X be a continuous mapping on a compact, path-connected, metric absolute neighborhood retract X. In the study of fixed point theorems, two numbers, namely the Lefschetz number L(f) and the Nielsen number N(f), play a very important role. The relationships between these two numbers have not been extensively studied because of the fact that the Nielsen number is in general hard to compute. The first substantial result relating these two numbers was by Jiang This chapter discusses the fixed point property for a fiber preserving mapping of an orientable Hurewicz fibering (E, π, B). It presents the proof that if E satisfies the Jiang condition and a fiber preserving mapping f : E →E is such that if either fb : π–1 (b) →π–1 (b) or fB :B→B is homotopic to a fixed point free mapping, then f is homotopic to a fixed point free mapping.
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