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Authors: ASIF R. KHAN, JOSIP E. PEČARIĆ.
DOI: 10.24193/subbmath. 2021.4.02
Published Online: 2021-12-14
Published Print: 2021-12-30
pp. 613-627
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We consider positivity of sum $sum_{i=1}^np_if(x_i)$ involving convex functions of higher order. Analogous for integral $int_a^bp(x)f(g(x))dx$ is also given. Representation of a function $f$ via the Fink identity and the Green function leads us to identities for which we obtain conditions for positivity of the mentioned sum and integral. We obtain bounds for integral remainders which occur in those identities as well as corresponding mean value theorems.
Keywords:n-convex functions, Fink identity, Green function, Cebysev functional.
Mathematics Subject Classification (2010): 26A51, 26D15, 26D20.
