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Abstract and Applied Analysis

Volume 2013 (2013), Article ID 967132, 9 pages

http://dx.doi.org/10.1155/2013/967132

Research Article

## Some Fixed Point Theorems in -Metric Space Endowed with Graph

^{1}Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, Sector, H-12, Islamabad, Pakistan^{2}Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan^{3}Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

Received 6 July 2013; Revised 5 September 2013; Accepted 6 September 2013

Academic Editor: Douglas Anderson

Copyright © 2013 Maria Samreen 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

- I. A. Bakhtin, “The contraction mapping principle in almost metric spaces,”
*Journal of Functional Analysis*, vol. 30, pp. 26–37, 1989. - J. Heinonen,
*Lectures on Analysis on Metric Spaces*, Springer, New York, NY, USA, 2001. View at Publisher · View at Google Scholar · View at MathSciNet - N. Bourbaki,
*Topologie Generale*, Herman, Paris, France, 1974. - S. Czerwik, “Nonlinear set-valued contraction mappings in $b$-metric spaces,”
*Atti del Seminario Matematico e Fisico dell'Università di Modena*, vol. 46, no. 2, pp. 263–276, 1998. View at MathSciNet - M. Bota, A. Molnár, and C. Varga, “On Ekeland's variational principle in $b$-metric spaces,”
*Fixed Point Theory*, vol. 12, no. 1, pp. 21–28, 2011. View at MathSciNet - M. F. Bota-Boriceanu and A. Petruşel, “Ulam-Hyers stability for operatorial equations,”
*Analele Stiintifice ale Universitatii “Al. I. Cuza” din Iasi*, vol. 57, supplement 1, pp. 65–74, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - M. Păcurar, “A fixed point result for $\phi $-contractions on $b$-metric spaces without the boundedness assumption,”
*Polytechnica Posnaniensis. Institutum Mathematicum. Fasciculi Mathematici*, no. 43, pp. 127–137, 2010. View at MathSciNet - V. Berinde, “Sequences of operators and fixed points in quasimetric spaces,”
*Studia Universitatis Babeş-Bolyai*, vol. 41, no. 4, pp. 23–27, 1996. View at Zentralblatt MATH · View at MathSciNet - S. Banach, “Sur les operations dans les ensembles abstraits et leur application aux equations integrales,”
*Fundamenta Mathematicae*, vol. 3, pp. 133–181, 1922. - J. Jachymski, “The contraction principle for mappings on a metric space with a graph,”
*Proceedings of the American Mathematical Society*, vol. 136, no. 4, pp. 1359–1373, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - A. Petruşel and I. A. Rus, “Fixed point theorems in ordered l-spaces,”
*Proceedings of the American Mathematical Society*, vol. 134, no. 2, pp. 411–418, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - J. Matkowski, “Integrable solutions of functional equations,”
*Dissertationes Mathematicae*, vol. 127, p. 68, 1975. View at Zentralblatt MATH · View at MathSciNet - D. O'Regan and A. Petruşel, “Fixed point theorems for generalized contractions in ordered metric spaces,”
*Journal of Mathematical Analysis and Applications*, vol. 341, no. 2, pp. 1241–1252, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - R. P. Agarwal, M. A. El-Gebeily, and D. O'Regan, “Generalized contractions in partially ordered metric spaces,”
*Applicable Analysis*, vol. 87, no. 1, pp. 109–116, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - I. A. Rus,
*Generalized Contractions and Applications*, Cluj University Press, Cluj-Napoca, Romania, 2001. View at MathSciNet - V. Berinde,
*Contractii Generalizate si Aplicatii*, vol. 22, Editura Cub Press, Baia Mare, Romania, 1997. View at MathSciNet - V. Berinde, “Generalized contractions in quasimetric spaces,”
*Seminar on Fixed Point Theory*, vol. 3, pp. 3–9, 1993. View at Zentralblatt MATH - T. P. Petru and M. Boriceanu, “Fixed point results for generalized $\phi $-contraction on a set with two metrics,”
*Topological Methods in Nonlinear Analysis*, vol. 33, no. 2, pp. 315–326, 2009. View at MathSciNet - R. P. Agarwal, M. A. Alghamdi, and N. Shahzad, “Fixed point theory for cyclic generalized contractions in partial metric spaces,”
*Fixed Point Theory and Applications*, vol. 2012, article 40, 11 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet - A. Amini-Harandi, “Coupled and tripled fixed point theory in partially ordered metric spaces with application to initial value problem,”
*Mathematical and Computer Modelling*, vol. 57, no. 9-10, pp. 2343–2348, 2012. View at Publisher · View at Google Scholar · View at Scopus - H. K. Pathak and N. Shahzad, “Fixed points for generalized contractions and applications to control theory,”
*Nonlinear Analysis: Theory, Methods & Applications*, vol. 68, no. 8, pp. 2181–2193, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - S. M. A. Aleomraninejad, Sh. Rezapour, and N. Shahzad, “Some fixed point results on a metric space with a graph,”
*Topology and Its Applications*, vol. 159, no. 3, pp. 659–663, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - M. Samreen and T. Kamran, “Fixed point theorems for integral G-contractions,”
*Fixed Point Theory and Applications*, vol. 2013, article 149, 2013. - 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - G. Gwóźdź-Łukawska and J. Jachymski, “IFS on a metric space with a graph structure and extensions of the Kelisky-Rivlin theorem,”
*Journal of Mathematical Analysis and Applications*, vol. 356, no. 2, pp. 453–463, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - G. E. Hardy and T. D. Rogers, “A generalization of a fixed point theorem of Reich,”
*Canadian Mathematical Bulletin*, vol. 16, pp. 201–206, 1973. View at Zentralblatt MATH · View at MathSciNet - R. Kannan, “Some results on fixed points,”
*Bulletin of the Calcutta Mathematical Society*, vol. 60, pp. 71–76, 1968. View at Zentralblatt MATH · View at MathSciNet - S. K. Chatterjea, “Fixed-point theorems,”
*Doklady Bolgarskoĭ Akademii Nauk*, vol. 25, pp. 727–730, 1972. View at Zentralblatt MATH · View at MathSciNet - W. A. Kirk, P. S. Srinivasan, and P. Veeramani, “Fixed points for mappings satisfying cyclical contractive conditions,”
*Fixed Point Theory*, vol. 4, no. 1, pp. 79–89, 2003. View at Zentralblatt MATH · View at MathSciNet - M. Păcurar and I. A. Rus, “Fixed point theory for cyclic $\phi $-contractions,”
*Nonlinear Analysis: Theory, Methods & Applications*, vol. 72, no. 3-4, pp. 1181–1187, 2010. View at Publisher · View at Google Scholar · View at MathSciNet - F. Bojor, “Fixed point theorems for Reich type contractions on metric spaces with a graph,”
*Nonlinear Analysis: Theory, Methods and Applications*, vol. 75, no. 9, pp. 3895–3901, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus - M. A. Petric, “Some remarks concerning Ćirić-Reich-Rus operators,”
*Creative Mathematics and Informatics*, vol. 18, no. 2, pp. 188–193, 2009. View at Zentralblatt MATH · View at MathSciNet