EXISTENCE OF SOLUTION FOR A VOLTERRA TYPE INTEGRAL EQUATION USING DARBO-TYPE F-CONTRACTION

In this paper, we provide some generalizations of the Darbo's fixed point theorem and further develop notion $F$-contraction introduced by Wardowski in (\cite{wad}, D. Wardowski, \emph{Fixed points a new type contractive mappings complete metric spaces,} Fixed Point Theory Appl., 94, (2012)). To achieve this, introduce Darbo-type $F$-contraction, cyclic $(\alpha,\beta)$-admissible operator also establish common results for class framework Banach spaces. addition, apply our to existence solution Volterra integral equation.