Abstract
AbstractIn this paper, some generalizations of Darbo’s fixed point theorem are presented. An existence result for a class of fractional integral equations is given as an application of the obtained results.
Highlights
Introduction and preliminaries LetE be a Banach space over R with respect to a certain norm ·
For any subsets X and Y of E, we have the following notations: X denotes the closure of X; conv(X) denotes the convex hull of X; P(X) denotes the set of nonempty subsets of X; X + Y and λX (λ ∈ R) stand for algebraic operations on sets X and Y
If X is a nonempty subset of E and T : X → X is a given operator, we denote by Fix(T) the set of fixed points of T, that is, Fix(T) = {x ∈ X : Tx = x}
Summary
In [ ], Dhage introduced the following axiomatic definition of the measure of noncompactness. We say that σ is a D-measure of noncompactness (in the sense of Dhage) on E if the following conditions are satisfied:. In this paper, using the axiomatic definition of the measure of noncompactness given by Dhage, we obtain new generalizations of Theorem. The following lemma can be proved using a similar argument as in the proof of Theorem . Let IX be the set of mappings D : X → X such that (I ) D is continuous; (I ) there exists some φ ∈ such that σ (DW ).
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
