C*-Algebra-Valued Fuzzy Metric Spaces in Coupled Fixed Point with Applications

Theory of Approximation and Applications

مقاله 2، دوره 16، شماره 2، دی 2022، صفحه 7-13   

نوع مقاله: Research Articles

نویسنده

Samuel Adamariko Aniki^*

Department of Mathematics, Faculty of Science, Confluence University of Science and Technology, Osara, Kogi State, Nigeria

چکیده

Coupled fixed point has been a major area of research interest in the field of fixed point theory. This work establishes coupled fixed point for C*-algebra-valued contractions in fuzzy metric spaces. Also, application in integral equations to back up our claim was given. The results of our findings are an improvement to some existing works in the literature

کلیدواژه‌ها

Fixed point؛ Fuzzy metric space؛ Mixed monotone mapping؛ C*-algebra-valued contraction

مراجع

[1] Kamran T, Postolache M, Ghiura A, Batul S and Ali R, The Banach contraction principle in C*-algebra-valued b-metric spaces with application. Fixed Point Theory and Applications. 2016; 10. (Doi: 10.1186/s13663-015-0486-z)

[2] Bakhtin IA, The contraction mapping principle in quasimetric spaces. Functional Analysis. 1989; 30:26-37

[3] Czerwick S, Contraction mappings in b-metric spaces. Acta Math Inform Univ Ostrav. 1993; 1:5-11

[4] Czerwick S, Nonlinear set-valued contraction mappings in b-metric spaces. Atti Semin Mat Fis Univ Modena. 1998; 46:263-276

[5] Fang J, Common fixed point theorems of compatible and weakly compatible maps in Menger spaces. Nonlinear Anal. 2009; 5-6:1833-1843 (Doi: 10.1016/j.na.2009.01.018)

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

[7] 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)

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

[9] Kramosil I, Michalek J, Fuzzy metric and statistical metric spaces. Kybernetika. 1975; 11:326-333

[10] Cho Y,  Fixed points in fuzzy metric spaces. J Fuzzy Math. 1997; 5(4):949-962

[11] Gregori V, Sapena A, On fixed-point theorems in fuzzy metric spaces. Fuzzy Sets Syst. 2002; 125(2):245-252 (Doi: 10.1016/S0165-0114(00)00088-9)

 

[12] 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

[13] 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

[14] 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

[15] 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

[16] Beg I, Abbas M, Common fixed points of Banach operator pair on fuzzy normed spaces. Fixed Point Theory. 2011; 12(2):285-292

[17] Elagan SK, Rahmat MS, Some fixed points theorems in locally convex topology generated by fuzzy n-normed spaces. Iran J Fuzzy Syst. 2012; 9(4):43-54

[18] Khaogong C, Khammahawong K, Fixed point theorem in -algebra-valued fuzzy metric metric spaces with application. Thai Journal of Mathematics. 2021; 19(3):964-970

[19] Ma ZH, Jiang LN, Sun HK, C*-algebra-valued metric spaces and related fixed point theorems. Fixed Point Theory and Application. 2014; 206:1-11 (Doi: 10.1186/s13663-015-0471-6)

[20] Mihet D, On fuzzy contractive mappings in fuzzy metric spaces. Fuzzy Sets and Systems. 2007; 158:915-921 (Doi: 10.1016/j.fss.2006.11.012)