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, cilt.38, sa.5, ss.641-673, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 38 Sayı: 5
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1080/01630563.2017.1291522
  • Dergi Adı: NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.641-673
  • Anahtar Kelimeler: 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
  • İnönü Üniversitesi Adresli: Evet

Özet

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.