On fuzzy Volterra integral equations with deviating arguments (Q1774446)

Fuzzy integral equations were introduced by \textit{H. Y. Chen} [J. Math. Anal. Appl. 80, 19--30 (1981; Zbl 0506.45014)] and a survey of further results was presented by \textit{P. Diamond} [IEEE Trans. SMC 32 (1), 97--102 (2002)]. This paper is a continuation of the present authors' papers: [Indian J. Pure Appl. Math. 33, 329--343 (2002; Zbl 1005.45004); Bull. Calcutta Math. Soc. 94, 147--152 (2002; Zbl 1016.45003)]. Using the Darbo fixed point theorem [cf. \textit{G. Darbo}, Rend. Sem. Mat. Univ. Padova 24, 84--92 (1955; Zbl 0064.35704)], the authors prove the existence theorem for a fuzzy Volterra integral equation with delays. This result has mainly a theoretical meaning, because the Kuratowski measure of non-compactness used in assumptions of the theorem is rather difficult for the determination [cf. \textit{K. Goebel}, Concise course on fixed point theorems, Yokohama Publ., Yokohama (2002; Zbl 1066.47055)].