Topological Methods in Nonlinear Analysis

Krasnosel'skiĭ-Schaefer type method in the existence problems

Calogero Vetro and Dariusz Wardowski

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


We consider a general integral equation satisfying algebraic conditions in a Banach space. Using Krasnosel'skiĭ-Schaefer type method and technical assumptions, we prove an existence theorem producing a periodic solution of some nonlinear integral equation.

Article information

Topol. Methods Nonlinear Anal., Volume 54, Number 1 (2019), 131-139.

First available in Project Euclid: 16 July 2019

Permanent link to this document

Digital Object Identifier


Vetro, Calogero; Wardowski, Dariusz. Krasnosel'skiĭ-Schaefer type method in the existence problems. Topol. Methods Nonlinear Anal. 54 (2019), no. 1, 131--139. doi:10.12775/TMNA.2019.028.

Export citation


  • T.A. Burton, Integral equations, implicit functions, and fixed points, Proc. Amer. Math. Soc. 124 (1996), no. 8, 2383–2390.
  • T.A. Burton and C. Kirk, A fixed point theorem of Krasnoselskiĭ–Schaefer type, Math. Nachr. 189 (1998), 23–31.
  • Y. Liu and Z. Li, Schaefer type theorem and periodic solutions of evolution equations, J. Math. Anal. Appl. 316 (2006), 237–255.
  • H. Schaefer, Über die Methode der a priori-Schranken, Math. Ann. 129 (1955), 415–416.
  • C. Vetro and F. Vetro, The class of $F$-contraction mappings with a measure of noncompactness, Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness (J. Banas et al. eds.), Springer Singapore, 2017, pp. 297–331, DOI:10.1007/978-981-10-3722-1$\_$7
  • D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 94 (2012), 1–6.
  • D. Wardowski, Solving existence problems via $F$-contractions, Proc. Amer. Math. Soc. 146 (2018), 1585–1598.