Studying selected functional equations and inequalities on general structures and under possibly weak regularity assumptions. Applications of results obtained.
We have dealt with Hlawka’s inequality and Sincov inequality. We have proved that local boundedness of solutions of Hlawka’s inequality at zero implies their local boundedness on the whole domain. Similarly, continuity at zero together with vanishing at zero implies the continuity on the whole domain. Concerning Sincov inequality, we have proved a so-called support theorem, which implies that every solution of this inequality satisfying certain boundary conditions is expressible as a supremum of certain family of functions. What is more, we have demonstrated applications of Sincov inequality for some problems of the theory of binary gambling.
Włodzimierz Fechner, Żywilla Fechner, A functional equation motivated by some trigonometric identities, Journal of Mathematical Analysis and Applications, 449 (2) (2017), 1160-1171.
Włodzimierz Fechner, Hlawka’s functional inequality on topological groups, Banach Journal of Mathematical Analysis, 11/1 (2017), 130-142.
N.K.Agbeko, Włodzimierz Fechner, E. Rak, On lattice-valued maps stemming from the notion of optimal average, Acta Mathematica Hungarica, 152 (1) (2017), 72-83.
Włodzimierz Fechner, Ewa Rak, Lemnaouar Zedam, The modularity law in some classes of aggregation operators, Fuzzy Sets and Systems, 332 (2018), 56-73.
Włodzimierz Fechner, Richard’s inequality, Cauchy-Schwarz’s inequality and approximate solutions of Sincov’s equation, Proceedings of the American Mathematical Society 147/9 (2019), 3955-3960.
Włodzimierz Fechner, Sincov's inequalities on topological spaces, arXiv:1811.00303 [math.FA]
Włodzimierz Fechner, New inequalities for probability functions in the two-person red-and-black game, arXiv:1811.00359 [math.PR]
Włodzimierz Fechner, On a functional inequality stemming from the Grüss-type inequalities, arXiv:1906.01928 [math.CA]