Applications of Measure of Noncompactness and Darbo's Fixed Point Theorem to Nonlinear Integral Equations in Banach Spaces. (4th May 2017)

• Record Type: Journal Article
• Authors: Çakan, Ümit; Özdemir, İsmet
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 5(2017)
• Page Start: 641
• Page End: 673
• Publication Date: 2017-05-04
• Subjects: Darbo fixed-point theorem -- Fixed point theorem in Banach algebra -- Measure of noncompactness -- Nonlinear integral equations -- Riemann–Liouville fractional integral; 26A33 -- 45M99 -- 47H08 -- 47H10; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1291522
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: We prove a theorem on the existence of solutions of some nonlinear functional integral equations in the Banach algebra of continuous functions on the interval [0, a ]. Then we consider a nonlinear integral equation of fractional order and give some sufficient conditions for existence of solutions of this equation. We use fixed point theorems associated with the measure of noncompactness as the main tool. Our existence results include several results obtained in previous studies. Finally we present some examples which show that our results are applicable.