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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 967132, 9 pages
Some Fixed Point Theorems in -Metric Space Endowed with Graph
1Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, Sector, H-12, Islamabad, Pakistan
2Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan
3Department 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.
- 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.
- N. Bourbaki, Topologie Generale, Herman, Paris, France, 1974.
- S. Czerwik, “Nonlinear set-valued contraction mappings in -metric spaces,” Atti del Seminario Matematico e Fisico dell'Università di Modena, vol. 46, no. 2, pp. 263–276, 1998.
- M. Bota, A. Molnár, and C. Varga, “On Ekeland's variational principle in -metric spaces,” Fixed Point Theory, vol. 12, no. 1, pp. 21–28, 2011.
- 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.
- M. Păcurar, “A fixed point result for -contractions on -metric spaces without the boundedness assumption,” Polytechnica Posnaniensis. Institutum Mathematicum. Fasciculi Mathematici, no. 43, pp. 127–137, 2010.
- V. Berinde, “Sequences of operators and fixed points in quasimetric spaces,” Studia Universitatis Babeş-Bolyai, vol. 41, no. 4, pp. 23–27, 1996.
- 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.
- 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.
- J. Matkowski, “Integrable solutions of functional equations,” Dissertationes Mathematicae, vol. 127, p. 68, 1975.
- 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.
- 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.
- I. A. Rus, Generalized Contractions and Applications, Cluj University Press, Cluj-Napoca, Romania, 2001.
- V. Berinde, Contractii Generalizate si Aplicatii, vol. 22, Editura Cub Press, Baia Mare, Romania, 1997.
- V. Berinde, “Generalized contractions in quasimetric spaces,” Seminar on Fixed Point Theory, vol. 3, pp. 3–9, 1993.
- T. P. Petru and M. Boriceanu, “Fixed point results for generalized -contraction on a set with two metrics,” Topological Methods in Nonlinear Analysis, vol. 33, no. 2, pp. 315–326, 2009.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- R. Kannan, “Some results on fixed points,” Bulletin of the Calcutta Mathematical Society, vol. 60, pp. 71–76, 1968.
- S. K. Chatterjea, “Fixed-point theorems,” Doklady Bolgarskoĭ Akademii Nauk, vol. 25, pp. 727–730, 1972.
- 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.
- M. Păcurar and I. A. Rus, “Fixed point theory for cyclic -contractions,” Nonlinear Analysis: Theory, Methods & Applications, vol. 72, no. 3-4, pp. 1181–1187, 2010.
- 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.
- M. A. Petric, “Some remarks concerning Ćirić-Reich-Rus operators,” Creative Mathematics and Informatics, vol. 18, no. 2, pp. 188–193, 2009.