A New Type Of Contractıon Vıa Measure Of Non-Compactness Wıth An Applıcatıon To Volterra Integral Equatıon

Abstract

Darbo fixed point theorem is a powerful tool which is used in many fields in mathemati s. Be ause 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-contration of Darbo type mapping and define a new contration 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 contration, which we all F-Darbo type contration, has more general results than many already studied in the literature. Further-more, we explain the results of F-Darbo type contration mapping with an interesting example. Finally, we give an application to solve the Volterra-type integral equation with the new type contration. © 2022. Publications de l''Institut Mathematique. All Rights Reserved.