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

Ahmed A. F. Soliman | Zendy

Open Access

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

Author(s) -

Ahmed A. F. Soliman

Publication year - 2017

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1707949s

Subject(s) - mathematics , semigroup , banach space , nonlinear system , fixed point theorem , fixed point , uniform continuity , uniform boundedness , bounded function , regular polygon , mathematical analysis , pure mathematics , exponential stability , metric space , physics , geometry , quantum mechanics

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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