The staff of the Department do research on selected problems in the following domains: nonlinear analysis, convex analysis and applied topology.<\/p>\n
Several problems of widely understood nonlinear analysis are investigated. There are discussed topics concerning
\nnonlinear differential and integral equations (e.g. Hammerstein, Volterra integral equations and
\neguations of fractional order) as regards the existence and uniqueness of solutions in various classes (e.g. in
\nclasses of almost periodic functions of various types like Bohr almost periodic functions, Bochner a.p. functions,
\nStepanov a.p. functions and Levitan a.p. functions or in classes of functions of bounded variation in the sense
\nof Jordan or Young) and topological properties of solution sets (in particular, the so-called Aronszajn type
\ntheorems). Quite a lot of attention is paid to some problems of the operator theory (most of all to the superposition
\noperators) and some problems of formal analysis, as well. Moreover, topics concerning the fixed point theory for
\nfunctions and multifunctions as well as selected topics from the range of the point-set topology are discussed
\n(e.g. among others, hyperconvex spaces, R-trees, measures of noncompactness etc.)<\/p>\n
Another direction of research are algebraic, analytic, geometrical and topological properties of pairs of closed
\nconvex sets (e.g. the translation property, shadowing of sets, Sallee sets etc.) and minimal pairs (as regards the
\nexistence and uniqueness up to translation), Minkowski-Radstr\u00f6m-H\u00f6rmander spaces over any Hausdorff topological
\nvector space and quasidifferential calculus, as well (e.g. sublinear functions along with their differences).
\nMoroever, there are also discussed some applications of Minkowski-Radstr\u00f6m-H\u00f6rmander spaces e.g. in the theory of
\nmultifunctions or to the description of the growth of crystals.<\/p>\n","protected":false},"excerpt":{"rendered":"
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 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/zants.wmi.amu.edu.pl\/en\/wp-json\/wp\/v2\/pages\/7"}],"collection":[{"href":"https:\/\/zants.wmi.amu.edu.pl\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/zants.wmi.amu.edu.pl\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/zants.wmi.amu.edu.pl\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/zants.wmi.amu.edu.pl\/en\/wp-json\/wp\/v2\/comments?post=7"}],"version-history":[{"count":1,"href":"https:\/\/zants.wmi.amu.edu.pl\/en\/wp-json\/wp\/v2\/pages\/7\/revisions"}],"predecessor-version":[{"id":8,"href":"https:\/\/zants.wmi.amu.edu.pl\/en\/wp-json\/wp\/v2\/pages\/7\/revisions\/8"}],"wp:attachment":[{"href":"https:\/\/zants.wmi.amu.edu.pl\/en\/wp-json\/wp\/v2\/media?parent=7"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}