Alternative proof of Mulholland’s theorem and new solutions to Mulholland inequality

0395238 - ÚI 2014 RIV US eng C - Conference Paper (international conference)
Petrík, Milan - Navara, M. - Sarkoci, P.
Alternative proof of Mulholland’s theorem and new solutions to Mulholland inequality.
ISMVL 2013. IEEE 43rd International Symposium on Multiple-Valued Logic. Los Alamitos: IEEE Computer Society, 2013, s. 346-351. ISBN 978-0-7695-4976-7. ISSN 0195-623X.
[ISMVL 2013. IEEE International Symposium on Multiple-Valued Logic /43./. Toyama (JP), 22.05.2013-24.05.2013]
R&D Projects: GA ČR GAP202/10/1826
Grant - others:CTU(CZ) SGS12/187/OHK3/3T/13
Institutional support: RVO:67985807
Keywords : dominance relation * Minkowski inequality * Mulholland inequality * triangular norm
Subject RIV: BA - General Mathematics

Mulholland inequality is a real functional inequality presented in 1950 in a paper by Mulholland as a generalization of the Minkowski inequality. In his paper, Mulholland has also provided a sufficient condition for the inequality to be satisfied. However, until now, it has remained an open problem whether this sufficient condition is also necessary. This paper investigates a geometric interpretation of Mulholland inequality and offers a class of functions satisfying the inequality which is strictly larger compared to the class delimited by the Mulholland’s condition. Thus, it is proven that the condition is not necessary.
Permanent Link: http://hdl.handle.net/11104/0223328