A Simultaneous System of Functional Inequalities and Mappings Which Are Weakly of a Constant Sign
نویسندگان
چکیده
It is shown that, under some algebraic conditions on fixed reals α1, α2, . . . , αn+1 and vectors a1,a2, . . . ,an+1 ∈ R, every continuous at a point function f : R → R satisfying the simultaneous system of inequalities f(x + ai) ≤ αi + f(x), x ∈ R, i = 1, 2, . . . , n + 1, has to be of the form f(x) = p · x + f(0), x ∈ R, with uniquely determined p ∈ R. For mappings with values in a Banach space which are weakly of a constant sign, a counterpart of this result is given.
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