Abstract
The strong Schur-convexity of the integral mean as well as of the left and right gaps in the Hermite–Hadamard inequality for strongly convex functions are proved. An useful characterization of strongly Schur-convex functions \(F:I^n \rightarrow {\mathbb R}\) by partial derivatives is given. As an application, a result on the strong Schur-concavity of the integral mean of the digamma function is obtained.
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The authors would like to thank the anonymous reviewer for comments that improved the paper.
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This publication was supported by the University of Bielsko-Biala, Department of Mathematics, and University of Split, Faculty of Science.
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Adamek, M., Klaričić Bakula, M. & Nikodem, K. Strong Schur-Convexity of the Integral Mean. Results Math 78, 58 (2023). https://doi.org/10.1007/s00025-023-01836-3
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DOI: https://doi.org/10.1007/s00025-023-01836-3