Applications of Measure of Noncompactness and Darbo's Fixed Point Theorem to Nonlinear Integral Equations in Banach Spaces

ÇAKAN Ü., Ozdemir I.

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, vol.38, no.5, pp.641-673, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 38 Issue: 5
  • Publication Date: 2017
  • Doi Number: 10.1080/01630563.2017.1291522
  • Journal Name: NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.641-673
  • Keywords: Darbo fixed-point theorem, Fixed point theorem in Banach algebra, Measure of noncompactness, Nonlinear integral equations, Riemann-Liouville fractional integral, FRACTIONAL ORDER, MONOTONIC SOLUTIONS, LINEAR MODIFICATION, VOLTERRA TYPE, EXISTENCE, ATTRACTIVITY, SOLVABILITY, BEHAVIOR, ARGUMENT
  • Inonu University Affiliated: Yes

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.