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**Superadditivity, monotonicity, and exponential convexity of the Petrović-type functionals.**
*(English)*
Zbl 1245.26012

Summary: We consider functionals derived from Petrović-type inequalities and establish their superadditivity, subadditivity, and monotonicity properties on the corresponding real \(n\)-tuples. By virtue of established results we also define some related functionals and investigate their properties regarding exponential convexity. Finally, the general results are then applied to some particular settings.

### MSC:

26D20 | Other analytical inequalities |

### References:

[1] | J. E. Pe, F. Proschan, and Y. L. Tong, Convex Functions, Partial Orderings, and Statistical Applications, vol. 187 of Mathematics in Science and Engineering, Academic Press, Boston, Mass, USA, 1992. · Zbl 0749.26004 |

[2] | S. Bernstein, “Sur les fonctions absolument monotones,” Acta Mathematica, vol. 52, no. 1, pp. 1-66, 1929. · JFM 55.0142.07 · doi:10.1007/BF02547400 |

[3] | N. I. Akhiezer, The Classical Moment Problem and Some Related Questions in Analysis, Oliverand Boyd, Edinburgh, UK, 1965. · Zbl 0257.30024 |

[4] | D. S. Mitrinović and J. E. Pe, “On some inequalities for monotone functions,” Unione Matematica Italiana. Bollettino B, vol. 5, no. 2, pp. 407-416, 1991. · Zbl 0725.26012 |

[5] | D. S. Mitrinović, J. E. Pe, and A. M. Fink, Classical and New Inequalities in Analysis, vol. 61 of Mathematics and its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1993. · Zbl 0771.26009 |

[6] | M. Anwar, J. Jak, J. Pe, and A. Ur Rehman, “Exponential convexity, positive semi-definite matrices and fundamental inequalities,” Journal of Mathematical Inequalities, vol. 4, no. 2, pp. 171-189, 2010. · Zbl 1218.26007 |

[7] | S. Butt, J. Pe, and A. Rehman, “Exponential convexity of Petrović and related functional,” Journal of Inequalities and Applications, vol. 89, 16 pages, 2011. · Zbl 1278.46058 |

[8] | J. Jak and J. Pe, “Exponential convexity method,” Submitted. |

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