Journal of Applied Analysis Vol. 1, No. 2, pp. 205211 (1995) 

Fixed point and approximate fixed point theorems for nonaffine mapsL. Gajek, J. Jachymski and D. ZagrodnyInstitute of MathematicsTechnical University of Lodz al. Politechniki 11 90924 Lodz, Poland Abstract: Let $C$ be a nonempty subset of a linear topological space $X$, and $T$ be a selfmap of $C$ such that the range of $IT$ is convex, where $I$ denotes the identity map on X. We give conditions under which a map $T$ has a fixed point or a $V$fixed point (i.e. a point $x_{0}\in C$ such that $Tx_{0}\in x_{0}+V$, where $V$ is a neighborhood of the origin). Our theorems generalize the recent results of M. Edelstein and K.K. Tan. As an application we provide a simple proof of the MarkovKakutani theorem. We also establish a common $V$fixed point theorem for commuting affine maps (possibly discontinuous). Keywords: Fixed point, $V$fixed point, convex set, close range, affine map,commuting maps, common fixed point, common $V$fixed point Classification (MSC2000): 47H10, 47A99, 47H99 Full text of the article:
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