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Fixed points and best approximation in Menger convex metric spaces

Ismat Beg, Mujahid Abbas (2005)

Archivum Mathematicum

We obtain necessary conditions for the existence of fixed point and approximate fixed point of nonexpansive and quasi nonexpansive maps defined on a compact convex subset of a uniformly convex complete metric space. We obtain results on best approximation as a fixed point in a strictly convex metric space.

Fixed points, eigenvalues and surjectivity for (ws)-compact operators on unbounded convex sets

Afif Amar (2013)

Open Mathematics

The paper studies the existence of fixed points for some nonlinear (ws)-compact, weakly condensing and strictly quasibounded operators defined on an unbounded closed convex subset of a Banach space. Applications of the newly developed fixed point theorems are also discussed for proving the existence of positive eigenvalues and surjectivity of quasibounded operators in similar situations. The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness.

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