Fixed Point Theorems in Cone Metric Spaces via c-Distance Over Topological Module
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Abstract
In 2011, Wang and Guo introduced c-distance in cone metric spaces. The idea of cone metric spaces over topological modules was presented by Branga and Olaru in 2020. Combining these two ideas, we introduce cone metric spaces with c-distance over topological module and establish a fixed point theorem.
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References
- M. Abbas, G. Jungck, Common Fixed Point Results for Noncommuting Mappings Without Continuity in Cone Metric Spaces, J. Math. Anal. Appl. 341 (2008), 416–420, https://doi.org/10.1016/j.jmaa.2007.09.070.
- M. Abbas, B. E. Rhoades, Fixed and Periodic Point Results in Cone Metric Spaces, Appl. Math. Lett. 22 (2009), 511–515, https://doi.org/10.1016/j.aml.2008.07.001.
- A. Azam, M. Arshad, Common Fixed Points of Generalized Contractive Maps in Cone Metric Spaces, Bull. Iran. Math. Soc. 35 (2009), 255–264.
- A.N. Branga, I.M. Olaru, Cone Metric Spaces Over Topological Module and Fixed Point Theorems for Lipschitz Mappings, Mathematics, 8 (2020), 724. https://doi.org/10.3390/math8050724.
- L. Ciric, H. Lakzian, V. Rakocevic, Fixed Point Theorems for w-Cone Distance Contraction Mappings in tvs-Cone Metric Spaces, Fixed Point Theory Appl. 2012 (2012), 3. https://doi.org/10.1186/1687-1812-2012-3.
- M. Dordevic, D. Doric, Z. Kadelburg, S. Radenovic, D. Spasic, Fixed Point Results Under c-Distance in tvs-Cone Metric Spaces, Fixed Point Theory Appl. 2011 (2011), 29. https://doi.org/10.1186/1687-1812-2011-29.
- Z.M. Fadail, A.G.B. Ahmad, Z. Golubovic, Fixed Point Theorems of Single-Valued Mapping for c-Distance in Cone Metric Spaces, Abstr. Appl. Anal. 2012 (2012), 826815. https://doi.org/10.1155/2012/826815.
- A.M.W. Glass, Partially Ordered Groups, World Scientific, (1999). https://doi.org/10.1142/3811.
- L.G. Huang, X. Zhang, Cone Metric Spaces and Fixed Point Theorems of Contractive Mappings, J. Math. Anal. Appl. 332 (2007), 1468–1476. https://doi.org/10.1016/j.jmaa.2005.03.087.
- D. Ilic, V. Rakocevic, Common Fixed Points for Maps on Cone Metric Space, J. Math. Anal. Appl. 341 (2008), 876–882. https://doi.org/10.1016/j.jmaa.2007.10.065.
- D. Ilic, V. Rakocevic, Quasi-Contraction on a Cone Metric Space, Appl. Math. Lett. 22 (2009), 728–731. https://doi.org/10.1016/j.aml.2008.08.011.
- S. Jankovic, Z. Kadelburg, S. Radenovic, On Cone Metric Spaces: A Survey, Nonlinear Anal.: Theory Methods Appl. 74 (2011), 2591–2601. https://doi.org/10.1016/j.na.2010.12.014.
- O. Kada, T. Suzuki, W. Takahashi, Non-Convex Minimization Theorems and Fixed Point Theorems in Complete Metric Spaces, Math. Japon. 44 (1996), 381-391. https://cir.nii.ac.jp/crid/1570009749812799360.
- Z. Kadelburg, S. Radenovic, Some Common Fixed Point Results in Non-Normal Cone Metric Spaces, J. Nonlinear Sci. Appl. 3 (2010), 193–202.
- Z. Kadelburg, S. Radenovic, V. Rakocevic, Topological Vector Space-Valued Cone Metric Spaces and Fixed Point Theorems, Fixed Point Theory Appl. 2010 (2010), 170253. https://doi.org/10.1155/2010/170253.
- Z. Kadelburg, S. Radenovic, Coupled Fixed Point Results Under tvs-Cone Metric and w-Cone-Distance, Adv. Fixed Point Theory, 2 (2012), 29-46.
- S.A. Steinberg, Lattice-ordered Rings and Modules, Springer, New York, (2010). https://doi.org/10.1007/978-1-4419-1721-8.
- S. Wang, B. Guo, Distance in Cone Metric Spaces and Common Fixed Point Theorems, Appl. Math. Lett. 24 (2011), 1735-1739. https://doi.org/10.1016/j.aml.2011.04.031.
- D. Wardowski, Endpoints and Fixed Points of Set-Valued Contractions in Cone Metric Spaces, Nonlinear Anal.: Theory Methods Appl. 71 (2009), 512-516. https://doi.org/10.1016/j.na.2008.10.089.
- S. Warner, Topological Rings, North-Holland, Amsterdam, 1993.