Abstract and Applied Analysis

On Weakly ( C , ψ , ϕ ) -Contractive Mappings in Ordered Partial Metric Spaces

Erdal Karapınar and Wasfi Shatanawi

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Abstract

We introduce the notion of weakly ( C , ψ , ϕ ) -contractive mappings in ordered partial metric spaces and prove some common fixed point theorems for such contractive mappings in the context of partially ordered partial metric spaces under certain conditions. We give some common fixed point results of integral type as an application of our main theorem. Also, we give an example and an application of integral equation to support the useability of our results.

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 495892, 17 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1355495842

Digital Object Identifier
doi:10.1155/2012/495892

Mathematical Reviews number (MathSciNet)
MR2965467

Zentralblatt MATH identifier
1246.54044

Citation

Karapınar, Erdal; Shatanawi, Wasfi. On Weakly $(C,\psi ,\varphi )$ -Contractive Mappings in Ordered Partial Metric Spaces. Abstr. Appl. Anal. 2012 (2012), Article ID 495892, 17 pages. doi:10.1155/2012/495892. https://projecteuclid.org/euclid.aaa/1355495842


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References

  • S. G. Matthews, “Partial metric topology,” in Proceedings of the 8th Summer Conference on General Topology and its Applications, Queen's College (1992), vol. 728, pp. 183–197, Annals of the New York Academy of Sciences, 1994.\setlengthemsep0.5pt
  • T. Abdeljawad, E. Karap\inar, and K. Taş, “Existence and uniqueness of a common fixed point on partial metric spaces,” Applied Mathematics Letters, vol. 24, no. 11, pp. 1900–1904, 2011.
  • Th. Abdeljawad, E. Karap\inar, and K. Taş, “A generalized contraction principle with control functions on partial metric spaces,” Computers & Mathematics with Applications, vol. 63, no. 3, pp. 716–719, 2012.
  • Th. Abdeljawad, “Fixed points for generalized weakly contractive mappings in partial metric spaces,” Mathematical and Computer Modelling, vol. 54, no. 11-12, pp. 2923–2927, 2011.
  • I. Altun and A. Erduran, “Fixed point theorems for monotone mappings on partial metric spaces,” Fixed Point Theory and Applications, vol. 2011, Article ID 508730, 10 pages, 2011.
  • I. Altun and H. Simsek, “Some fixed point theorems on dualistic partial metric spaces,” Journal of Advanced Mathematical Studies, vol. 1, no. 1-2, pp. 1–8, 2008.
  • I. Altun, F. Sola, and H. Simsek, “Generalized contractions on partial metric spaces,” Topology and its Applications, vol. 157, no. 18, pp. 2778–2785, 2010.
  • I. Altun and K. Sadarangani, “Corrigendum to “Generalized contractions on partial metric spaces” [Topology Appl. 157 (2010) 2778–2785],” Topology and its Applications, vol. 158, no. 13, pp. 1738–1740, 2011.
  • H. Aydi, “Fixed point results for weakly contractive mappings in ordered partial metric spaces,” Journal of Advanced Mathematical Studies, vol. 4, no. 2, pp. 1–12, 2011.
  • H. Aydi, “Some coupled fixed point results on partial metric spaces,” International Journal of Mathematics and Mathematical Sciences, vol. 2011, Article ID 647091, 11 pages, 2011.
  • H. Aydi, “Fixed point theorems for generalized weakly contractive condition in partially ordered metric spaces,” Journal of Nonlinear Analysis and Optimization, vol. 2, no. 2, pp. 33–48, 2011.
  • H. Aydi, E. Karap\inar, and W. Shatanawi, “Coupled fixed point results for $(\psi ,\phi )$-weakly contractive condition in ordered partial metric spaces,” Computers & Mathematics with Applications, vol. 62, no. 12, pp. 4449–4460, 2011.
  • A. G. Bin Ahmad, Z. M. Fadail, V. Ć. Rajić, and S. Radenović, “Nonlinear contractions in 0-complete partial metric spaces,” Abstract and Applied Analysis. In press.
  • L. Ćirić, B. Samet, H. Aydi, and C. Vetro, “Common fixed points of generalized contractions on partial metric spaces and an application,” Applied Mathematics and Computation, vol. 218, no. 6, pp. 2398–2406, 2011.
  • Z. Golubović, S. Kadelburg, and Radenović, “Coupled coincidence points of mappings in partially ordered metric spaces,” Abstract and Applied Analysis, vol. 2012, Article ID 192581, 18 pages, 2012.
  • E. Karap\inar, “Generalizations of Caristi Kirk's theorem on partial metric spaces,” Fixed Point Theory and Applications, vol. 2011, p. 4, 2011.
  • E. Karap\inar and U. Yüksel, “Some common fixed point theorems in partial metric spaces,” Journal of Applied Mathematics, vol. 2011, Article ID 263621, 16 pages, 2011.
  • E. Karap\inar, “A note on common fixed point theorems in partial metric spaces,” Miskolc Mathematical Notes, vol. 12, no. 2, pp. 185–191, 2011.
  • E. Karap\inar, N. Shobkolaei, S. Sedghi, and S. M. Vaezpour, “A common fixed point theorem for cyclic operators on partial metric spaces,” Filomat, vol. 26, no. 2, pp. 407–414, 2012.
  • K. P. Chi, E. Karapinar, and T. D. Thanh, “A generalized contraction principle in partial metric spaces,” Mathematical and Computer Modelling, vol. 55, no. 5-6, pp. 1673–1681, 2012.
  • E. Karap\inar, “Weak $\phi $-contraction on partial contraction,” Journal of Computational Analysis and Applications, vol. 14, no. 2, pp. 206–210, 2012.
  • E. Karap\inar, “Some fixed point theorems on the class of comparable partial metric spaces,” Applied General Topology, vol. 12, no. 2, pp. 187–192, 2011.
  • E. Karap\inar and M. Erhan, “Fixed point theorems for operators on partial metric spaces,” Applied Mathematics Letters, vol. 24, no. 11, pp. 1894–1899, 2011.
  • H. K. Nashine, Z. Kadelburg, and S. Radenović, “Common fixed point theorems for weakly isotone increasing mappings in partially ordered metric spaces,” Mathematical and Computer Modelling. In press.
  • 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.
  • S. Oltra and O. Valero, “Banach's fixed point theorem for partial metric spaces,” Rendiconti dell'Istituto di Matematica dell'Università di Trieste, vol. 36, no. 1-2, pp. 17–26, 2004.
  • S. Romaguera, “A Kirk type characterization of completeness for partial metric spaces,” Fixed Point Theory and Applications, vol. 2010, Article ID 493298, 6 pages, 2010.
  • B. Samet, M. Rajović, R. Lazović, and R. Stoiljković, “Common fixed point results for nonlinear contractions in partially ordered metric spaces,” Fixed Point Theory and Applications. In press.
  • W. Shatanawi and H. K. Nashine, “A generalization of Banach's contraction principle for nonlinear contraction in a partial metric space,” Journal of Nonlinear Science and Applications, vol. 5, pp. 37–43, 2012.
  • W. Shatanawi, H. K. Nashine, and N. Tahat, “Generalization of some coupled fixed point results on partial metric spaces,” International Journal of Mathematics and Mathematical Sciences, vol. 2012, Article ID 686801, 10 pages, 2012.
  • W. Shatanawi, B. Samet, and M. Abbas, “Coupled fixed point theorems for mixed monotone mappings in partially ordered metric spaces,” Mathematical and Computer Modelling, vol. 55, no. 3-4, pp. 680–687, 2012.
  • O. Valero, “On Banach fixed point theorems for partial metric spaces,” Applied General Topology, vol. 6, no. 2, pp. 229–240, 2005.
  • S. K. Chatterjea, “Fixed-point theorems,” Comptes Rendus de l'Académie Bulgare des Sciences, vol. 25, pp. 727–730, 1972.
  • B. S. Choudhury, “Unique fixed point theorem for weakly \emphC-contractive mappings,” Kathmandu University Journal of Science, Engineering and Technology, vol. 5, no. 1, pp. 6–13, 2009.
  • J. Harjani, B. López, and K. Sadarangani, “Fixed point theorems for weakly \emphC-contractive mappings in ordered metric spaces,” Computers & Mathematics with Applications, vol. 61, no. 4, pp. 790–796, 2011.
  • W. Shatanawi, “Fixed point theorems for nonlinear weakly \emphC-contractive mappings in metric spaces,” Mathematical and Computer Modelling, vol. 54, no. 11-12, pp. 2816–2826, 2011.
  • I. Altun and H. Simsek, “Some fixed point theorems on ordered metric spaces and application,” Fixed Point Theory and Applications, vol. 2010, Article ID 621469, 17 pages, 2010.
  • I. Altun, “Common fixed point theorems for weakly increasing mappings on ordered uniform spaces,” Miskolc Mathematical Notes, vol. 12, no. 1, pp. 3–10, 2011.
  • I. Altun and V. Rakočević, “Ordered cone metric spaces and fixed point results,” Computers & Mathematics with Applications, vol. 60, no. 5, pp. 1145–1151, 2010.
  • W. Shatanawi, “Some fixed point theorems in ordered \emphG-metric spaces and applications,” Abstract and Applied Analysis, Article ID 126205, 11 pages, 2011.
  • W. Shatanawi, “Some common coincidence point theorems on weakly increasing mappings in partially ordered cone metric spaces,” Gazi University Journal of Science, vol. 25, pp. 89–95, 2012.