GENERALIZED DARBO'S THEOREM AND ITS APPLICATION

In the present paper, using a mapping H : R+ -> R, we introduce a new type of set contraction called H-set contraction and prove a new fixed point theorem concerning H-set contraction which is a generalization of Darbo's fixed point theorem. For the some concrete mappings H, we obtain the set contractions of the type known from the literature and also k-set contraction. The article includes the examples of H-set contractions and some examples showing that the obtained extension is significant. We also show the applicability of the obtained results to the theory of functional integral equations.