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An extension of Mehta theorem with applications. (English) Zbl 1251.54059
In this paper, the authors extend the notion of measure of precompactness, introduced by {\it C. J. Himmelberg, J. R. Porter} and {\it F. S. Van Vleck} [Proc. Am. Math. Soc. 23, 635--641 (1969; Zbl 0195.14902)], to $l.c.$-spaces with precompact polytope and they obtain a generalization of Mehta’s theorem, see [{\it G. Mehta}, Appl. Math. Lett. 3, No. 2, 69--71 (1990; Zbl 0717.47020)]. Based on these results, the authors obtain a new fixed point result for a class of condensing mappings. This result is a generalization of a similar result from the paper {\it E. Tarafdar} and {\it P. J. Watson}, [Coincidence and the Fan-Glicksberg fixed point theorem in locally H-convex spaces. Research report, The University of Queensland, (1997)].

54H25Fixed-point and coincidence theorems in topological spaces
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
55M20Fixed points and coincidences (algebraic topology)
Full Text: DOI
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[10] E. Tarafdar, P.J. Watson, Coincidence and the Fan-Glicksberg fixed point theorem in locally H-convex spaces, Research report, The University of Queensland, 1997.
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