Fixed Point and Tripled Fixed Point Theorems under Pata-Type Conditions in Ordered Metric Spaces
Main Article Content
Abstract
In this paper, we first prove a version of the fixed point theorem obtained in [V. Pata, A fixed point theorem in metric spaces, J. Fixed Point Theory Appl. 10 (2011) 299-305], adjusted for monotone mappings in ordered metric spaces, as well as some generalizations. Then we apply them to obtain results of this type for tripled fixed points in two cases””for monotone and mixed-monotone mappings with three variables. An example is given to show the difference between some of these results.
Article Details
References
- V. Pata, A fixed point theorem in metric spaces. J. Fixed Point Theory Appl. 10 (2011) 299-305.
- M. Chakraborty, S. K. Samanta, A fixed point theorem for Kannan-type maps in metric spaces, arXiv:1211, 7331v2
- [math. GN] 16 Dec 2012.
- M. Eshaghi, S. Mohseni, M. R. Delavar, M. De La Sen, G. H. Kim, A. Arian, Pata contractions and coupled type fixed points. Fixed Point Theory Appl. 2014 (2014) Article ID 130.
- Z. Kadelburg, S. Radenovi ´c, Fixed point theorems for Pata-type maps in metric spaces, submitted.
- M. Paknazar, M. Eshaghi, Y. J. Cho, S. M. Vaezpour, A Pata-type fixed point theorem in modular spaces with application, Fixed Point Theory Appl. 2013(2013), Article ID 239.
- A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some application to matrix equations, Proc. Amer. Math. Soc. 132 (2004), 1435-1443.
- B. E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977) 257-290.
- S. Radenovi ´c, Z. Kadelburg, D. Jandrli ´c, A. Jandrli ´c, Some results on weak contraction maps, Bull. Iranian Math. Soc. 38(3) (2012), 625-645.
- M. Borcut, Tripled fixed point theorems for monotone mappings in partially ordered metric spaces, Carpathian J. Math. 28, 2 (2012), 207-214.
- V. Berinde, M. Borcut, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal. TMA 74 (2011), 4889-4897.
- A. Rold ´an, J. Mart ´inez-Moreno, C. Rold ´an, Multidimensional fixed point theorems in partially ordered complete metric spaces, J. Math. Anal. Appl. 396 (2012), 536-545.