Abstract
Using an extension of Montgomery’s identity and the Green’s function, we obtain new identities and related inequalities for weighted averages of n-convex functions, i.e. the sum \(\sum _{i=1}^m \rho _i h(\lambda _i)\) and the integral \(\int ^{b}_{a} \rho (\lambda ) h(\gamma (\lambda ))d\lambda \) where h is an n-convex function.
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The publication was supported by the Ministry of Education and Science of the Russian Federation (the Agreement number No. 02.a03.21.0008).
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Khan, A.R., Pečarić, J.E. & Praljak, M. Weighted averages of n-convex functions via extension of Montgomery’s identity. Arab. J. Math. 9, 381–392 (2020). https://doi.org/10.1007/s40065-019-0245-9
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DOI: https://doi.org/10.1007/s40065-019-0245-9