Copulas with given track and opposite track sections: Solution to a problem on diagonals

Alsina, 1993, On the characterization of a class of binary operations on distribution functions, Stat. Probab. Lett., 17, 85, 10.1016/0167-7152(93)90001-Y de Amo, 2012, Characterization of all copulas associated with non-continuous random variables, Fuzzy Sets Syst., 191, 103, 10.1016/j.fss.2011.10.005 de Amo, 2016, Characterization of copulas with given diagonal and opposite diagonal sections, Fuzzy Sets Syst., 284, 63, 10.1016/j.fss.2014.10.030 Bruckner, 1962, Some function classes related to the class of convex functions, Pac. J. Math., 12, 1203, 10.2140/pjm.1962.12.1203 De Baets, 2009, Opposite diagonal sections of quasi-copulas and copulas, Int. J. Uncertain. Fuzziness Knowl.-Based Syst., 15, 481, 10.1142/S0218488509006108 De Baets, 2011, Constructing copulas with given diagonal and opposite diagonal sections, Commun. Stat., Theory Methods, 40, 828, 10.1080/03610920903480866 Durante, 2011, A note on biconic copulas, Kybernetika, 47, 532 Durante, 2015 Durante, 2008, Semilinear copulas, Fuzzy Sets Syst., 15, 63, 10.1016/j.fss.2007.09.001 Fernández-Sánchez, 2016, The distribution of the probability mass of biconic copulas, Inf. Sci., 329, 177, 10.1016/j.ins.2015.09.026 2010 Jwaid, 2012, Biconic aggregation functions, Inf. Sci., 187, 129, 10.1016/j.ins.2011.10.012 Klement, 2005, Extensions to copulas and quasi-copulas as special 1-Lipschitz aggregation operators, Kybernetika, 41, 329 Maes, 2007, Orthosymmetrical monotone functions, Bull. Belg. Math. Soc. Simon Stevin, 14, 99, 10.36045/bbms/1172852247 Maes, 2009, Commutativity and self-duality: two tales of one equation, Int. J. Approx. Reason., 50, 189, 10.1016/j.ijar.2008.08.002 Mesiar, 2010, Open problems posed at the Tenth International Conference on Fuzzy Set Theory and Applications, Kybernetika, 46, 585 Nelsen, 2006 Nelsen, 2008, On the construction of copulas and quasi-copulas with given diagonal sections, Insur. Math. Econ., 42, 473, 10.1016/j.insmatheco.2006.11.011 Rodríguez-Lallena, 2009, Some new characterizations and properties of quasi-copulas, Fuzzy Sets Syst., 160, 717, 10.1016/j.fss.2008.02.007 Sklar, 1959, Fonctions de répartition à n dimensions et leurs marges, Publ. Inst. Stat. Univ. Paris, 8, 229