Publications de l'Institut Mathematique 2022 Volume 111, Issue 125, Pages: 111-121
https://doi.org/10.2298/PIM2225111K
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A new type of contraction via measure of non-compactness with an application to Volterra integral equation
Karakaya Vatan (Department of Mathematical Engineering, Yildiz Technical University, Istanbul, Turkey), vkkaya@yahoo.com
Sekman Derya (Department of Mathematics, Ahi Evran University Kirsehir, Turkey), deryasekman@gmail.com
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 lasses and uniformly convergent
sequences of functions and examine some of its properties. Afterward, we
show that the new type of contraction, which we all 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.
Keywords: Volterra-type integral equation, Darbo fixed point theorem, F-contraction, measure of non compactness, sequences of functions
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