Abstract
The most famous of many problems in nonlinear analysis is Schauder's problem (Scottish book, problem 54) of the following form, that if C is a nonempty convex compact subset of a linear topological space does every continuous mapping / : C -* C has a fixed point? The answer we give in this paper is yes. In this paper we prove that if C is a nonempty convex compact subset of a linear topological space, then every continuous mapping / : C -> C has a fixed point. On the other hand, in this sense, we extend and connected former results of Brouwer, Schauder, Tychonoff, Markoff. Kakutani. Darbo. Sadovskij, Browder, Krasnoselskij, Ky Fan, Reinermann, Hukuhara, Ma-zur, Hahn, Ryll-Nardzewski, Day, Riedrich, Jahn, Eisenack-Fenske, Idzik. Kirk, Gohde, Caristi, Granas, Dugundji, Klee and some others.
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