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**Weighted Hermite-Hadamard and Simpson type inequalities for double integrals.**
*(English)*
Zbl 1483.26014

In this paper, the authors derive and prove a weighted identity for twice partially differenciable mapping. In addition, the derived identity was used to establish a weighted Hermite-Hadamard-type inequality for co-ordinated convex functions on \(\mathbb{R^2}\). Furthermore, some weighted generalizations of Hermite-Hadamard- and Simpson-type integral inequalities were established and well proved.

Reviewer: James Adedayo Oguntuase (Abeokuta)

### MSC:

26D07 | Inequalities involving other types of functions |

26D10 | Inequalities involving derivatives and differential and integral operators |

26D15 | Inequalities for sums, series and integrals |

26B15 | Integration of real functions of several variables: length, area, volume |

26B25 | Convexity of real functions of several variables, generalizations |

### Keywords:

Hermite-Hadamard-Fejer inequality; Simpson inequality; co-ordinated convex; integral inequalities
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\textit{H. Budak} et al., J. Math. Ext. 15, No. 1, 149--177 (2021; Zbl 1483.26014)

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