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In this paper, we study the existence of a common fixed point for uniformly continuous one parameter semigroup of nonlinear self-mappings on a closed convex subset C of a real Banach space X with uniformly normal structure such that the semigroup has a bounded orbit. This result applies, in particular, to study asymptotic stability criterion for a class of semigroup of nonlinear uniformly continuous infinite-dimensional systems.

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A common fixed point theorem for semigroups of nonlinear uniformly continuous mappings with an application to asymptotic stability of nonlinear systems