Analytical Analysis of Common Fixed Point Results in Fuzzy Cone Metric Spaces

Page Numbers: 294-303
Published: 2024-03-25
Digital Object Identifier: 10.58578/ajstea.v2i2.2804
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  • Surendra Kumar Tiwari Dr. C. V. Raman University, Bilaspur, India
  • Ranu Agrawal Dr. C. V. Raman University, Bilaspur, India

Abstract

The concept of fuzzy sets was introduced by Zadeh (1965) which marked the beginning of the evolution of fuzzy mathematics. The introduction of uncertainty in the theory of sets in a non-probabilistic manner opened up new possibilities for research in this field. Since then, many authors have explored the theory of fuzzy sets and its applications, leading to successful advancements in various fields such as mathematical programming, model theory, engineering sciences, image processing, and control theory. In this paper, we aim to improve and generalize some common fixed point theorems in fuzzy cone metric spaces, an extension of the well-known results given by Saif Ur Rahman and Hong Xu-Li (2017).

Keywords: Fuzzy metric space; Fuzzy Cone Metric Space; Fuzzy Cone Contractive Mapping
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Tiwari, S., & Agrawal, R. (2024). Analytical Analysis of Common Fixed Point Results in Fuzzy Cone Metric Spaces. Asian Journal of Science, Technology, Engineering, and Art, 2(2), 294-303. https://doi.org/10.58578/ajstea.v2i2.2804

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References

Abbas, M., Khan, A. and. Radenovic S. (2010). Common coupled fixed point theorems in cone metric spaces for w-compatible mappings, Appl. Math. Comp. 217, 195–202. http://dx.doi.org/10.1016/j.amc.2010.05.042

Ali, M. and Khanna,G.R. (2017). Intuitionistic fuzzy cone metric spaces and fixed point theorems, Int. J. Math. Appl., 5 (1-A), 25–36. http://ijmaa.in/

Altun, B. Damjanovic¸ B, and Djoric D. (2010). Fixed point and common fixed point theorems on ordered cone metric spaces, Appl. Math. Lett., 23, 310–316. doi:10.1016/j.aml.2009.09.016.

George, P. and Veeramani. (1994). on some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64 , 395–399. doi.org/10.1016/0165-0114(94)90162-7.

Grabiec, M. (1988). Fixed point in fuzzy metric spaces, Fuzzy Sets and Systems, 27, 385–389. http://dx.doi.org/10.1016/0165-0114(88)90064-4.

Hadzˇic´O. and Pap E. (2002). Fixed point theorem for multivalued mappings in probabilistic metric spaces and an applications in fuzzy metric spaces, Fuzzy Sets and Systems, 127, 333–344. https://doi.org/10.1016/S0165-0114 .

Huang, and Zhang. (2007). Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332, 1468–1476. https://doi.org/10.1016/j.jmaa.2005.03.087.

Jankovic S., Kadelburg, Z. and Radenovic S. (2011). on cone metric spaces: a survey, Nonlinear Anal., 74, 2591–2601. DOI:10.1016/j.na.2010.12.014.

Kiani, F. and Haradi, A.A. (2011). Fixed point and endpoint theorems for set-valued fuzzy contraction mapps in fuzzy metric spaces, Fixed Point Theory Appl., 2011, 9 pages.

Kramosil, J. Micha´lek. (1975). Fuzzy metric and statistical metric spaces, Kybernetika, 11, 336–344.

Latif A., Hussain, N. and Ahmad, J. (2016). Coincidence points for hybrid contractions in cone metric spaces, J. Nonlinear Convex Anal., 17, 899–906.

Li, Z.L. and Jiang, S. J. (2014). Quasi-contractions restricted with linear bounded mappings in cone metric spaces, Fixed Point Theory Appl., 2014, 10 pages.

Mehmood, N., Azam, A. Kocˇinac. (2015). Multivalued fixed point results in cone metric spaces, Topology Appl., 179, 156–170. shttps://doi.org/10.1016/j.topol.2014.07.011.

Nguyen, H. and Tran, D.T. (2014). Fixed point theorems and the Ulam-Hyers stability in non-Archimedean cone metric spaces, J. Math. Anal. Appl., 414, 10–20. DOI:10.1016/j.jmaa.2013.12.020.

Oner, T. (2016). On some results in fuzzy cone metric spaces, Int. J. Adv. Comput. Eng. Network., 4, 37–39.

Oner, T. (2016). On the metrizability of fuzzy cone metric spaces, Int. j. Eng. Technol. Manag. Appl. Sci., 2, 133–135.

Oner, T. Kandemire, M.B. and Tanay, B.Fuzzy cone meric spaces, J. Nonlinear Sci. Appl., 8 (2015), 610–616. https://www.researchgate.net/publication/277474776

N. Priyobarta, Y. Rohen, B. B. Upadhyay. (2016). Some fixed point results in fuzzy cone metric spaces, Int. J. Pure Appl. Math., 109, 573–582.doi:10.12732/ijpam.v109i3.7.

Sadeghi,Z, Vaezpour, S.M. Park,C., Saadati, R. and Vetro, C. (2014). Set-valued mappings in partially ordered fuzzy metric spaces, J. Inequal. Appl., 2014, 17 pages.http://www.journalofinequalitiesandapplications.com/content/2014/1/157

Schweizer, A. and Sklar. (1960). Statical metric spaces, Pac. J. Math., 10, 314–334. http://dx.doi.org/10.2140/pjm.1960.10.313.

Saif Ur Rehman and Hong-Xu Li. (2017). Fixed point theorems in fuzzy cone metric spaces, J. Nonlinears Sci. Appl.,5763-5769. doi:10.22436/jnsa.010.11.14

W. Shatanawi, E. Karapınar, H. Aydi. (2012). Coupled coincidence points in partially ordered cone metric spaces with a c-distance, J. Appl. Math., 2012, 15 pages.

Turkoglu, M. Abuloha. (2010). Cone metric spaces and fixed point theorems in diametrically contractive mappings, Acta Math. Sin.,26, 489–496.

L. A. Zadeh. (1965). sFuzzy sets, Information and Control, 8, 338–353. shttps://doi.org/10.1016/S0019-9958(65)90241-X.