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New solutions to Mulholland inequality

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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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References

  1. Alsina C., Frank M.J., Schweizer B.: Problems on associative functions. Aequationes Math., 66(1–2), 128–140 (2003)

    MATH  MathSciNet  Google Scholar 

  2. Baricz, Á.: Geometrically concave univariate distributions. J. Math. Anal. Appl., 363(1), 182–196 (2010) doi:10.1016/j.jmaa.2009.08.029

  3. Jarczyk W., Matkowski J.: On Mulholland’s inequality. Proc. Am. Math. Soc., 130(11), 3243–3247 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  4. Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms, vol. 8 of trends in logic. Kluwer Academic Publishers, Dordrecht (2000)

  5. Kuczma M.: An introduction to the theory of functional equations and inequalities. Cauchys equation and Jensens inequality. Uniwersytet Ślaşki, Polish Scientific Publishers, Warszawa-Kraków-Katowice (1985)

    Google Scholar 

  6. Matkowski, J.: L p-like paranorms. In: Selected topics in functional equations and iteration theory. Proceedings of the Austrian-Polish Seminar, Graz, 1991, Grazer Math. Ber. 316, 103–138 (1992)

  7. Menger, K.: Statistical metrics. Proc. Nat. Acad. Sci. USA 8, 535–537 (1942)

  8. Mulholland H.P.: On generalizations of Minkowski’s inequality in the form of a triangle inequality. Proc. Lond. Math. Soc. 51(2), 294–307 (1947)

    MathSciNet  Google Scholar 

  9. Sarkoci P.: Dominance is not transitive on continuous triangular norms. Aequationes Math. 75, 201–207 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  10. Sarkoci, P.: Dominance relation for conjunctors in fuzzy logic. Ph.D. thesis (2007)

  11. Schweizer B., Sklar A.: Probabilistic metric spaces. Dover Publications, Mineola (2005)

    Google Scholar 

  12. Sklar A.: Remark and problem, report of meeting, 37th International Symposium on functional equations (Huntington, 1999). Aequationes Math. 60, 187–188 (2000)

    Google Scholar 

  13. Tardiff R.M.: On a generalized Minkowski inequality and its relation to dominates for t-norms. Aequationes Math. 27(3), 308–316 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  14. Tardiff R.M.: Topologies for probabilistic metric spaces. Pacific J. Math 65, 233–251 (1976)

    Article  MATH  MathSciNet  Google Scholar 

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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

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