Abstract and Applied Analysis

An Application of Fixed Point Theory to a Nonlinear Differential Equation

A. P. Farajzadeh, A. Kaewcharoen, and S. Plubtieng

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 introduce a new family of mappings on [ 0 , + ) by relaxing the nondecreasing condition on the mappings and by using the properties of this new family we present some fixed point theorems for α - ψ -contractive-type mappings in the setting of complete metric spaces. By applying our obtained results, we also assure the fixed point theorems in partially ordered complete metric spaces and as an application of the main results we provide an existence theorem for a nonlinear differential equation.

Article information

Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 605405, 7 pages.

First available in Project Euclid: 27 February 2015

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Farajzadeh, A. P.; Kaewcharoen, A.; Plubtieng, S. An Application of Fixed Point Theory to a Nonlinear Differential Equation. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 605405, 7 pages. doi:10.1155/2014/605405. https://projecteuclid.org/euclid.aaa/1425049480

Export citation


  • M. Abbas, G. V. R. Babu, and G. N. Alemayehu, “On common fixed points of weakly compatible mappings satisfying generalized condition (B),” Filomat, vol. 25, no. 2, pp. 9–19, 2011.
  • M. Abbas and G. Jungck, “Common fixed point results for noncommuting mappings without continuity in cone metric spaces,” Journal of Mathematical Analysis and Applications, vol. 341, no. 1, pp. 416–420, 2008.
  • E. Karapinar and B. Samet, “Generalized $\alpha -\psi $-contractive type mappings and related fixed point theorems with applications,” Abstract and Applied Analysis, vol. 2012, Article ID 793486, 17 pages, 2012.
  • P. Salimi, A. Latif, and N. Hussain, “Modified $\alpha $-$\varphi $-contractive mappings with applications,” Fixed Point Theory and Applications, vol. 2013, article 151, 2013.
  • B. Samet, C. Vetro, and P. Vetro, “Fixed point theorems for $\alpha $-$\psi $-contractive type mappings,” Nonlinear Analysis, vol. 75, no. 4, pp. 2154–2165, 2012.
  • S. Banach, “Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales,” Fundamenta Mathematicae, vol. 3, pp. 133–181, 1922.
  • R. Caccioppoli, “Un teorema generale sullesistenza di elementi uniti in una trasformazione funzionale,” Rendicontilincei: Matematica E Applicazioni, vol. 11, pp. 794–799, 1930.
  • R. Kannan, “Some results on fixed points,” Bulletin of the Calcutta Mathematical Society, vol. 10, pp. 71–76, 1968.
  • T. Gnana Bhaskar and V. Lakshmikantham, “Fixed point theorems in partially ordered metric spaces and applications,” Nonlinear Analysis: Theory, Methods & Applications, vol. 65, no. 7, pp. 1379–1393, 2006.
  • A. Branciari, “A fixed point theorem for mappings satisfying a general contractive condition of integral type,” International Journal of Mathematics and Mathematical Sciences, vol. 29, no. 9, pp. 531–536, 2002.
  • V. Lakshmikantham and L. Ćirić, “Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces,” Nonlinear Analysis, vol. 70, no. 12, pp. 4341–4349, 2009.
  • J. J. Nieto and R. Rodríguez-López, “Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations,” Order, vol. 22, no. 3, pp. 223–239, 2005.
  • H. L. Royden, Real Analysis, Prentice Hall, 3rd edition, 1988.
  • A. C. M. Ran and M. C. B. Reurings, “A fixed point theorem in partially ordered sets and some applications to matrix equations,” Proceedings of the American Mathematical Society, vol. 132, no. 5, pp. 1435–1443, 2004. \endinput