Abstract
The notion of \((m,M,\Psi )\)-Schur-convexity is introduced and functions generating \((m,M,\Psi )\)-Schur-convex sums are investigated. An extension of the Hardy–Littlewood–Pólya majorization theorem is obtained. A counterpart of the result of Ng stating that a function generates \((m,M,\Psi )\)-Schur-convex sums if and only if it is \((m,M,\psi )\)-Wright-convex is proved and a characterization of \((m,M,\psi )\)-Wright-convex functions is given.
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Dedicated to Professor Karol Baron on his 70th birthday.
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Dragomir, S.S., Nikodem, K. Functions generating (m,M,\(\varvec{\Psi }\))-Schur-convex sums. Aequat. Math. 93, 79–90 (2019). https://doi.org/10.1007/s00010-018-0569-0
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DOI: https://doi.org/10.1007/s00010-018-0569-0