A new type of contraction via measure of non-compactness with an application to Volterra integral equation

Vatan Karakaya, Derya Sekman

Darbo fixed point theorem is a powerful tool which is used in many fields in mathematics. Because of this feature, many generalizations of this theorem and its relations with other subjects have been investigated. Here we introduce a generalization of an $F$-contraction of Darbo type mapping and define a new contraction by using both function classes and uniformly convergent sequences of functions and examine some of its properties. Afterward, we show that the new type of contraction, which we call $F$-Darbo type contraction, has more general results than many already studied in the literature. Furthermore, we explain the results of $F$-Darbo type contraction mapping with an interesting example. Finally, we give an application to solve the Volterra-type integral equation with the new type contraction.