- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Journal of Mathematics
Volume 2013 (2013), Article ID 295093, 8 pages
Some Fixed Point Theorems for Prešić-Hardy-Rogers Type Contractions in Metric Spaces
1Department of Applied Mathematics, Shri Vaishnav Institute of Technology and Science, Gram Baroli, Sanwer Road, Indore 453331, India
2Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, Serbia
Received 2 January 2013; Accepted 7 February 2013
Academic Editor: NanJing Huang
Copyright © 2013 Satish Shukla 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.
- R. Kannan, “Some results on fixed points,” Bulletin of the Calcutta Mathematical Society, vol. 60, pp. 71–76, 1968.
- R. Kannan, “Some results on fixed points. II,” The American Mathematical Monthly, vol. 76, pp. 405–408, 1969.
- S. Reich, “Some remarks concerning contraction mappings,” Canadian Mathematical Bulletin, vol. 14, pp. 121–124, 1971.
- S. K. Chatterjea, “Fixed-point theorems,” Comptes Rendus de l'Académie Bulgare des Sciences, vol. 25, pp. 727–730, 1972.
- L. B. Ćirić, “Generalized contractions and fixed-point theorems,” Publications de l'Institut Mathématique, vol. 12, no. 26, pp. 19–26, 1971.
- 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.
- S. B. Prešić, “Sur une classe d'inéquations aux différences finies et sur la convergence de certaines suites,” Publications de l'Institut Mathématique, vol. 5, no. 19, pp. 75–78, 1965.
- S. B. Prešić, “Sur la convergence des suites,” Comptes Rendus de l'Académie des Sciences, vol. 260, pp. 3828–3830, 1965.
- L. B. Ćirić and S. B. Prešić, “On Prešić type generalization of the Banach contraction mapping principle,” Acta Mathematica Universitatis Comenianae, vol. 76, no. 2, pp. 143–147, 2007.
- M. Pãcurar, “A multi-step iterative method for approximating common fixed points of Prešić-Rus type operators on metric spaces,” Studia Universitatis Babes-Bolyai, Mathematica, vol. 55, no. 1, p. 149, 2010.
- M. Păcurar, “Approximating common fixed points of Presić-Kannan type operators by a multi-step iterative method,” Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica, vol. 17, no. 1, pp. 153–168, 2009.
- M. Păcurar, “Common fixed points for almost Presić type operators,” Carpathian Journal of Mathematics, vol. 28, no. 1, pp. 117–126, 2012.
- M. S. Khan, M. Berzig, and B. Samet, “Some convergence results for iterative sequences of Prešić type and applications,” Advances in Difference Equations, vol. 2012, article 38, 2012.
- R. George, K. P. Reshma, and R. Rajagopalan, “A generalised fixed point theorem of Presic type in cone metric spaces and application to Markov process,” Fixed Point Theory and Applications, vol. 2011, article 85, 2011.
- S. Shukla, R. Sen, and S. Radenović, “Set-valued Prešić type contraction in metric spaces,” Analele Stiintifice ale Universitatii. In press.
- S. Shukla and R. Sen, “Set-valued Prešić-Reich type mappings in metric spaces,” Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales A, 2012.
- S. K. Malhotra, S. Shukla, and R. Sen, “A generalization of Banach contraction principle in ordered cone metric spaces,” Journal of Advanced Mathematical Studies, vol. 5, no. 2, pp. 59–67, 2012.
- Y.-Z. Chen, “A Prešić type contractive condition and its applications,” Nonlinear Analysis, vol. 71, no. 12, pp. e2012–e2017, 2009.
- B. E. Rhoades, “A comparison of various definitions of contractive mappings,” Transactions of the American Mathematical Society, vol. 226, pp. 257–290, 1977.
- H. Aydi, E. Karapınar, and B. Samet, “Remarks on some recent fixed point theorems,” Fixed Point Theory and Applications, vol. 2012, article 76, 2012.