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Fixed point theory in symmetric spaces with applications to probabilistic spaces. (English) Zbl 0947.54022
The main purpose of this paper is to present Jungck type fixed point theorems [G. Jungck, Am. Math. Mon. 83, 261-263 (1976; Zbl 0321.54025); the reviewer, Math. Semin. Notes, Kobe Univ. 7, 91-97 (1979; Zbl 0419.54029)] in general probabilistic structures. Indeed, the authors obtain common fixed point theorems for symmetric spaces and then present these results in probabilistic analysis. Subsequently, several results from G. Jungck [loc. cit.], the first author [Math. Jap. 44, No. 3, 487-493 (1996; Zbl 0868.47048)], the reviewer [loc. cit.] and elsewhere are generalized.

54H25Fixed-point and coincidence theorems in topological spaces
54E70Probabilistic metric spaces
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47S50Operator theory in probabilistic metric linear spaces