Abstract and Applied Analysis

Fixed Point Results for α-ψ-Contractive Mappings Including Almost Contractions and Applications

Gonca Durmaz, Gülhan Mınak, and Ishak Altun

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Abstract

In the recent paper (B. Samet, C. Vetro, and P. Vetro, Fixed point theorems for α - ψ -contractive type mappings, Nonlinear Analysis. Theory, Methods and Applications, 75 (2012), 2154-2165.), the authors introduced the concept of α -admissible maps on metric spaces. Using this new concept, they presented some nice fixed point results. Also, they gave an existence theorem for integral equation to show the usability of their result. Then, many authors focused on this new concept and obtained a lot of fixed point results, which are used for existence theorems. In this paper, we not only extend some of the recent results about this direction but also generalize them. Then, we give some examples to show our results are proper extensions. Furthermore, we use our results to obtain the existence and uniqueness result for a solution of fourth order two-point boundary value problem.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 869123, 10 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412606561

Digital Object Identifier
doi:10.1155/2014/869123

Mathematical Reviews number (MathSciNet)
MR3246363

Zentralblatt MATH identifier
07023226

Citation

Durmaz, Gonca; Mınak, Gülhan; Altun, Ishak. Fixed Point Results for α - ψ -Contractive Mappings Including Almost Contractions and Applications. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 869123, 10 pages. doi:10.1155/2014/869123. https://projecteuclid.org/euclid.aaa/1412606561


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References

  • V. Berinde, Iterative Approximation of Fixed Points, Springer, Berlin, Germany, 2007.
  • B. Samet, C. Vetro, and P. Vetro, “Fixed point theorems for $\alpha -\psi -$contractive type mappings,” Nonlinear Analysis. Theory, Methods & Applications, vol. 75, no. 4, pp. 2154–2165, 2012.
  • J. H. Asl, S. Rezapour, and N. Shahzad, “On fixed points of $\alpha $-$\psi $-contractive multifunctions,” Fixed Point Theory and Applications, vol. 2012, article 212, p. 6, 2012.
  • 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.
  • B. Mohammadi, S. Rezapour, and N. Shahzad, “Some results on fixed points of $\alpha $-$\psi $-Ciric generalized multifunctions,” Fixed Point Theory and Applications, vol. 2013, article 24, 10 pages, 2013.
  • N. Hussain, E. Karap\inar, P. Salimi, and F. Akbar, “$\alpha $-admissible mappings and related fixed point theorems,” Journal of Inequalities and Applications, vol. 2013, article 114, 11 pages, 2013.
  • V. Berinde, “Approximating fixed points of weak $\varphi $-contractions using the Picard iteration,” Fixed Point Theory, vol. 4, no. 2, pp. 131–147, 2003.
  • V. Berinde, “On the approximation of fixed points of weak contractive mappings,” Carpathian Journal of Mathematics, vol. 19, no. 1, pp. 7–22, 2003.
  • V. Berinde, “General constructive fixed point theorems for Ćirić-type almost contractions in metric spaces,” Carpathian Journal of Mathematics, vol. 24, no. 2, pp. 10–19, 2008.
  • V. Berinde, “Some remarks on a fixed point theorem for Ćirić-type almost contractions,” Carpathian Journal of Mathematics, vol. 25, no. 2, pp. 157–162, 2009.
  • M. Pacurar, “Sequences of almost contractions and fixed points,” Carpathian Journal of Mathematics, vol. 24, no. 2, pp. 101–109, 2008.
  • M. Pacurar, “Remark regarding two classes of almost contractions with unique fixed point,” Creative Mathematics and Informatics, vol. 19, no. 2, pp. 178–183, 2010.
  • J. Caballero, J. Harjani, and K. Sadarangani, “Uniqueness of positive solutions for a class of fourth-order boundary value pro-blems,” Abstract and Applied Analysis, vol. 2011, Article ID 543035, 13 pages, 2011.
  • M. Pei and S. K. Chang, “Monotone iterative technique and symmetric positive solutions for a fourth-order boundary value problem,” Mathematical and Computer Modelling, vol. 51, no. 9-10, pp. 1260–1267, 2010. \endinput