• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1725-1740
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• 2008

In this paper, we introduce a fixed point index of weakly inward 1-set-contraction mappings. With the aid of the new index, we obtain some new fixed point theorems, nonzero fixed point theorems and multiple positive fixed points for this class of mappings. As an application of nonzero fixed point theorems, we discuss an eigenvalue problem.