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Fixed point theorems for generalized set-contraction maps and their applications. (English) Zbl 1225.54012
Summary: A new generalized set-valued contraction on topological spaces with respect to a measure of noncompactness is introduced. Two fixed point theorems for the KKM type maps which are either generalized set-contraction or condensing ones are given. Furthermore, applications of these results to the existence of coincidence points and maximal elements are deduced.

54H25Fixed-point and coincidence theorems in topological spaces
54C50Special sets of topological spaces defined by functions
47H08Measures of noncompactness and condensing mappings, $K$-set contractions, etc.
Full Text: DOI
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