Polynomial selections and separation by polynomials
classification
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math.CA
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polynomialfunctionsrealresultseparationanotherapplicationconditions
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Necessary and sufficient conditions under which two real functions defined on the real interval can be separated by a polynomial are given. An immediate consequence of the main result is the existence of the polynomial separation of convex functions of higher order. Another application is some Hyers-Ulam-stability-type result.
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