A Common Fixed Point Theorem for Semigroups of Nonlinear Uniformly Continuous Mappings with an Application to Asymptotic Stability of Nonlinear Systems

Ahmed Hussein Soliman


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

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