On sums of linear and bounded mappings
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We give a necessary and sufficient condition in order that a mapf from a real linear space into a real Banach space should have the formf =L + r withL being a linear operator andr being a bounded perturbation.
KeywordsLinear Operator Functional Equation Bound Mapping Real Banach Space Homogeneous Mapping
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- Jo. Tabor, On approximately linear mappings. In:“Stability of Hyers-Ulam type”, A Volume dedicated to D. H. Hyers & S. Ulam, (ed. Th. M. Rassias and J. Tabor), Hadronic Press, Inc., Palm Harbor (1994), 157–163.Google Scholar