An Extension of Mixed Monotone Mapping to Tripled Fixed Point Theorem in Fuzzy Metric Spaces

Subject Areas : Fixed Point Theory and its Applications

Samuel Aniki ¹ , Sheidu Momoh ²

1 - Department of Mathematics, Faculty of Science, Confluence University of Science and Technology, Osara, Kogi State, Nigeria
2 - Department of Mathematics, Federal University Lokoja, Kogi State, Nigeria

Received: 2022-05-18 Accepted : 2022-07-15 Published : 2022-05-01

Keywords: Existence and uniqueness, tripled fixed point, Mixed monotone mapping, Fuzzy metric space,

Abstract :

In this paper, we prove the concept of fuzzy metric spaces of tripled fixed point via mixed monotone mappings and prove the existence and uniqueness theorem for contractive type mapping. In order to do that, we consider a modification to results on tripled fixed point theorem in fuzzy metric spaces available in literature. Additionally, we prove some tripled fixed point theorems for metric spaces via mixed monotone mappings. These results extend and generalize some recent results in literature.

References:

[1] Bhaskar T, Lakshmikantham V, Fixed point theorems in partially ordered metric spaces and applications. Nonlinear Anal. 2006; 65(7):1379-1393 (Doi: 10.1016/j.na.2005.10.017)

[2] Zadeh L, Fuzzy sets. Inf Control. 1965; 8:338-353 (Doi: 10.1016/S0019-9958(65)90241-X)

[3] George A, Veeramani P, On some results in fuzzy metric spaces. Fuzzy Sets Syst. 1994; 64:395-399 (Doi: 10.1016/0165-0114(94)90162-7)

[4] Kramosil I, Michalek J, Fuzzy metric and statistical metric spaces. Kybernetika. 1995; 11:326-333

[5] Hu, X, Common coupled fixed point theorems for contractive mappings in fuzzy metric spaces. Fixed Point Theory Appl. 2011;  363716 (Doi: 10.1155/2011/363716)

[6] Zhu X, Xiao J, Note on “Coupled fixed point theorems for contractions in fuzzy metric spaces”. Nonlinear Anal. 2011; 74(16):5475-5479 (Doi: 10.1016/j.na.2011.05.034)

[7] Berinde V, Borcut M, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces. Nonlinear Anal. 2011; 74:4889-4897 (Doi: 10.1016/j.na.2011.03.032)

[8] Borcut M, Berinde V, Tripled coincidence theorems for contractive type mappings in partially ordered metric spaces. Appl Math Comput. 2012; 218:5929-5936 (Doi: 10.1016/j.amc.2011.11.049)

[9] Aydi H, Karapınar E, Postolache M, Tripled coincidence theorems for weak ϕ-contractions in partially ordered metric spaces. Fixed Point Theory Appl. 2012; 44 (Doi: 10.1186/1687-1812-2012-44)

[10] Izadikhah, M., Farzipoor Saen, R. Solving voting system by data envelopment analysis for assessing sustainability of suppliers. Group Decis Negot, 2019, 28, P. 641–669. Doi: 10.1007/s10726-019-09616-7

[11] Poordavoodi, A., Reza, M., Haj, H., Rahmani, A. M., Izadikhah, M., Toward a More Accurate Web Service Selection Using Modified Interval DEA Models with Undesirable Outputs. CMES-Computer Modeling in Engineering & Sciences, 2020, 123(2), P. 525–570. Doi: 10.32604/cmes.2020.08854

[12] Azadi, M., Izadikhah, M., Ramezani, F., Hussain, F.K., A mixed ideal and anti-ideal DEA model: an application to evaluate cloud service providers, IMA Journal of Management Mathematics, 2000, 31(20), P. 233–256, Doi: 10.1093/imaman/dpz012

[13] Izadikhah, M. Financial Assessment of Banks and Financial Institutes in Stock Exchange by Means of an Enhanced Two stage DEA Model. Advances in Mathematical Finance and Applications, 2021, 6(2), P. 207-232. Doi: 10.22034/amfa.2020.1910507.1491

[14] Karapınar E, Luong N, Quadruple fixed point theorems for nonlinear contractions. Comput Math Appl. 2012; 64:1839-1848 (Doi: 10.1016/j.camwa.2012.02.061)

[15] Karapınar E, Berinde V, Quadruple fixed point theorems for nonlinear contractions in partially ordered metric spaces. Banach J Math Anal. 2012; 6:74-89 (Doi: 10.15352/bjma/1337014666)

[16] Roldan A, Martinez-Moreno J, Roldan, C, Multidimensional fixed point theorems in partially ordered complete metric spaces. J Math Anal Appl. 2012; 396: 536-545 (Doi: 10.1016/j.jmaa.2012.06.049)

[17] Roldan A, Martinez-Moreno J, Roldan C, Multidimensional coincidence point results for compatible mappings in partially ordered fuzzy metric spaces. Fuzzy Sets Syst. 2013; (Doi: 10.1016/j.fss.2013.10.009)

[18] Roldan A, Martinez-Moreno J, Roldan C, Tripled fixed point theorem in fuzzy metric spaces and applications. Fixed Point Theory and Applications. 2013; 2013:29 (Doi:10.1186/1687-1812-2013-29)

[19] Hadzic O, Pap E, Fixed point theory in probabilistic metric spaces. Dordrecht: Kluwer Academic; 2001.