Abstract
The aim of this paper is to introduce a new condition of expansiveness which extends the class of the known expansive-type mappings in the domain of closed and bounded subsets of a metric space. For the sum of an expansive mapping in a proposed sense defined on a closed convex and bounded subset of a Banach space and a continuous and compact operator, there are proved some fixed point theorems. There are also provided some examples which motivate our research. Moreover, an application to the existence problem of periodic solutions of nonlinear integral equations with a rational part is provided.
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