In this paper, the authors extend the notion of measure of precompactness, introduced by C. J. Himmelberg, J. R. Porter
and F. S. Van Vleck
[Proc. Am. Math. Soc. 23, 635–641 (1969; Zbl 0195.14902
-spaces with precompact polytope and they obtain a generalization of Mehta’s theorem, see [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 E. Tarafdar
and P. J. Watson
, [Coincidence and the Fan-Glicksberg fixed point theorem in locally H-convex spaces. Research report, The University of Queensland, (1997)].