The staff of the Department do research on selected problems in the following domains: nonlinear analysis, convex analysis and applied topology.
Several problems of widely understood nonlinear analysis are investigated. There are discussed topics concerning
nonlinear differential and integral equations (e.g. Hammerstein, Volterra integral equations and
eguations of fractional order) as regards the existence and uniqueness of solutions in various classes (e.g. in
classes of almost periodic functions of various types like Bohr almost periodic functions, Bochner a.p. functions,
Stepanov a.p. functions and Levitan a.p. functions or in classes of functions of bounded variation in the sense
of Jordan or Young) and topological properties of solution sets (in particular, the so-called Aronszajn type
theorems). Quite a lot of attention is paid to some problems of the operator theory (most of all to the superposition
operators) and some problems of formal analysis, as well. Moreover, topics concerning the fixed point theory for
functions and multifunctions as well as selected topics from the range of the point-set topology are discussed
(e.g. among others, hyperconvex spaces, R-trees, measures of noncompactness etc.)
Another direction of research are algebraic, analytic, geometrical and topological properties of pairs of closed
convex sets (e.g. the translation property, shadowing of sets, Sallee sets etc.) and minimal pairs (as regards the
existence and uniqueness up to translation), Minkowski-Radström-Hörmander spaces over any Hausdorff topological
vector space and quasidifferential calculus, as well (e.g. sublinear functions along with their differences).
Moroever, there are also discussed some applications of Minkowski-Radström-Hörmander spaces e.g. in the theory of
multifunctions or to the description of the growth of crystals.