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In this note, we give solutions to Problems $9.4$ and $9.5,$ which werepresented by Mesiar and Stup\v{n}anov\'{a} [{\it Open problems from the 12thInternational Conference on Fuzzy Set Theory and Its Applications}, Fuzzy Setsand Systems 261 (2015)] and by Borzov\'a-Moln\'arov\'a, Hal\u{c}inov\'a andHutn\'ik, in [{\it The smallest semicopula-based universal integrals I:properties and characterizations,} Fuzzy Sets and Systems (2014),http://dx.doi.org/ 10.1016/j.fss.2014.09.024].

Convergence theorems for seminormed fuzzy integrals: Solutions to Hutn\`ik's open problems