Asif R. KHAN, Josip E. PECARIC, Marjan PRALJAK, Sanja VAROSANEC

Positivity of sums and integrals for n-convex functions via the Fink identity

We consider the positivity of the sum ∑nρi?(ξi) , where ? is a convex function of higher order, aswell as analogous results involving the integral b0 ρ(ξ)?(g(ξ))dξ . We use a representation of the function ? via the Fink identity and the Green function that leads us to identities from which we obtain conditions for positivity of the above-mentioned sum and integral. We also obtain bounds for the integral remainders which occur in these identities, as well as corresponding mean value results.

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ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

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