Fractional order Taylor's series and the neo-classical inequality
classification
🧮 math.CA
math.PR
keywords
inequalityneo-classicalfractionaloptimalorderseriestaylorapplication
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We prove the neo-classical inequality with the optimal constant, which was conjectured by T. J. Lyons [Rev. Mat. Iberoamericana 14 (1998) 215-310]. For the proof, we introduce the fractional order Taylor's series with residual terms. Their application to a particular function provides an identity that deduces the optimal neo-classical inequality.
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