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New solutions to Mulholland inequality

Abstract

The paper gives answer to two open questions related to Mulholland’s inequality. First, it is shown that there exists a larger set of solutions to Mulholland’s inequality compared to the one delimited by Mulholland’s condition. Second, it is demonstrated that the set of functions solving Mulholland’s inequality is not closed with respect to compositions.

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Correspondence to Milan Petrík.

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This work was completed with the support of our \({{\rm T_EX}}\) -pert.

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Petrík, M. New solutions to Mulholland inequality. Aequat. Math. 89, 1107–1122 (2015). https://doi.org/10.1007/s00010-014-0327-x

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  • DOI: https://doi.org/10.1007/s00010-014-0327-x

Mathematics Subject Classification

  • Primary 26D07
  • Secondary 39B72
  • 26D15
  • 26A51
  • 03E72
  • 54E70

Keywords

  • Convex function
  • dominance of strict triangular norms
  • geometrically convex function
  • Minkowski inequality
  • Mulholland inequality
  • probabilistic metric spaces