Conjecture on Fixed Points Indices of Positive Mappings in Cones
Li Dongsheng, Li Kaitai
(Xi'an Jiaotong University, Xi'an 710049, China)

Abstract: Discussed is a conjecture on fixed points indices of mappins in cones proposed by E. N. Dancer. The geometric property of cones is first described by using functionals under the condition that the cone has nonempty interior points. The conjecture is then proved by the perturbation method of operators. An example is given to illustrate how the theory can be applied.
Keywords: fixed point index;cone;positive mapping