Table of Contents Author Guidelines Submit a Manuscript
The Scientific World Journal
Volume 2014, Article ID 541862, 9 pages
http://dx.doi.org/10.1155/2014/541862
Research Article

Existence of Tripled Fixed Points for a Class of Condensing Operators in Banach Spaces

1Department of Mathematical Engineering, Faculty of Chemistry-Metallurgical, Yildiz Technical University, 34210 Istanbul, Turkey
2Department of Mathematics, Faculty of Science and Letters, Yildiz Technical University, 34210 Istanbul, Turkey

Received 28 May 2014; Accepted 23 June 2014; Published 14 September 2014

Academic Editor: S. A. Mohiuddine

Copyright © 2014 Vatan Karakaya et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. K. Kuratowski, “Sur les espaces complets,” Fundamenta Mathematicae, vol. 15, pp. 301–309, 1930. View at Google Scholar
  2. J. Banaś and K. Goebel, Measures of noncompactness in Banach Spaces, vol. 60 of Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 1980. View at MathSciNet
  3. R. Agarwal, M. Meehan, and D. O'Regan, Fixed Point Theory and Applications, Cambridge University Press, 2004.
  4. A. Aghajani, J. Banaś, and Y. Jalilian, “Existence of solutions for a class of nonlinear Volterra singular integral equations,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 1215–1227, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. A. Aghajani and Y. Jalilian, “Existence and global attractivity of solutions of a nonlinear functional integral equation,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 11, pp. 3306–3312, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. J. Banaś, “Measures of noncompactness in the study of solutions of nonlinear differential and integral equations,” Central European Journal of Mathematics, vol. 10, no. 6, pp. 2003–2011, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. J. Banaś and B. Rzepka, “An application of a measure of noncompactness in the study of asymptotic stability,” Applied Mathematics Letters, vol. 16, no. 1, pp. 1–6, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. M. Mursaleen and S. A. Mohiuddine, “Applications of measures of noncompactness to the infinite system of differential equations in lp space,” Nonlinear Analysis: Theory, Methods & Applications, vol. 75, no. 4, pp. 2111–2115, 2012. View at Publisher · View at Google Scholar
  9. A. Aghajani, R. Allahyari, and M. Mursaleen, “A generalization of Darbo's theorem with application to the solvability of systems of integral equations,” Journal of Computational and Applied Mathematics, vol. 260, pp. 68–77, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  10. J. Banaś, “On measures of noncompactness in Banach spaces,” Commentationes Mathematicae Universitatis Carolinae, vol. 21, no. 1, pp. 131–143, 1980. View at Google Scholar · View at MathSciNet
  11. S. S. Chang, Y. J. Cho, and N. J. Huang, “Coupled fixed point theorems with applications,” Journal of the Korean Mathematical Society, vol. 33, no. 3, pp. 575–585, 1996. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. R. R. Akhmerov, M. I. Kamenski, A. S. Potapov, A. E. Rodkina, and B. N. Sadovski, Measures of Noncompactness and Condensing Operators, vol. 55, Birkhauser, Basel, Switzerland, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  13. A. Aghajani and N. Sabzali, “Existence of coupled fixed points via measure of noncompactness and applications,” Journal of Nonlinear and Convex Analysis, vol. 15, no. 5, pp. 953–964, 2014. View at Google Scholar
  14. V. Berinde and M. Borcut, “Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 15, pp. 4889–4897, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus