## Abstract

In this paper we extend the well known Heinz inequality which says that (formula presented) where (formula presented) We discuss the bounds of H(t) in the intervals t [1, 2] and t [2, ) using the subquadracity and the superquadracity of φ(x) = x^{t}, x ≥ 0 respectively. Further, we extend H(t) to get results related to (formula presented) a_{n+1} = a_{1}, a_{i} > 0, i = 1, n, where H_{1}(t) = H(t). These results, obtained by using rearrangement techniques, show that the minimum and the maximum of the sum (formula presented) for a given t, depend only on the specific arrangements called circular alternating order rearrangement and circular symmetrical order rearrangement of a given set (formula presented) a_{i} > 0, i = 1, 2, n. These lead to extended Heinz type inequalities of (formula presented) for different intervals of t. The results may also be considered as special cases of Jensen type inequalities for concave, convex, subquadratic and superquadratic functions, which are also discussed in this paper.

Original language | English |
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Title of host publication | Operator Theory |

Subtitle of host publication | Advances and Applications |

Publisher | Springer Science and Business Media Deutschland GmbH |

Pages | 1-14 |

Number of pages | 14 |

DOIs | |

State | Published - 2021 |

### Publication series

Name | Operator Theory: Advances and Applications |
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Volume | 282 |

ISSN (Print) | 0255-0156 |

ISSN (Electronic) | 2296-4878 |

### Bibliographical note

Publisher Copyright:© 2021, Springer Nature Switzerland AG.

## Keywords

- Convexity
- Heinz inequality
- Jensen inequality
- Rearrangements
- Superquadracity

## ASJC Scopus subject areas

- Analysis