Abstract:
In this paper, we provide some generalizations of the Darbo’s fixed
point theorem and further develop the notion of F-contraction introduced by
Wardowski in ( [22], D. Wardowski, Fixed points of a new type of contractive
mappings in complete metric spaces, Fixed Point Theory and Appl., 94, (2012)).
To achieve this, we introduce the notion of Darbo-type F-contraction, cyclic
(α, β)-admissible operator and we also establish some fixed point and common
fixed point results for this class of mappings in the framework of Banach spaces.
In addition, we apply our fixed point results to establish the existence of solution to a Volterra type integral equation.
