Fixed point results in tricomplex valued fuzzy metric spaces with application

Authors and Affiliations

  • Rakesh Tiwari
  • Shraddha Rajput SSTC.Bhilai

About this article

Download PDF

Abstract

In this article, accredit the innovative concept of complex valued the fuzzy set due to Ramot et al.[17], Singh et al.[20] and Choi et al.[7], we introduce the conceptualisation of tricomplex valued fuzzy metric spaces and this paper is inspired by Ismat Beg et al.[10]. Various related topological features have been established for tricomplex-valued fuzzy metric spaces, thereby reinforcing the foundational concept.

References

[1] Azam A., Fisher B. and Khan M., “Common fixed point theorems in complex valued metric spaces”, Num. Func. Anal. Opt., 32(2011),243−253.

[2] Banach S., “Sur les operations dans les ensembles abstraits et leur application aux ´ equations int ´ egrals”, ´ Fundam. Math., 3(1922),133−181. URL:

htt p : //matwbn.icm.edu.pl/ksiazki/or/or2/or215.pd f.

[3] Buckley J.J., “Fuzzy complex numbers”, in Proc ISFK, Guangzhou, China, (1987),597 ˆaAˇS¸700.

[4] Buckley J.J., “Fuzzy complex numbers”, Fuzzy Sets Syst, 33(1989),333 ˆaAˇS¸345.

View more references (28)

[5] Buckley J.J., “Fuzzy complex analysis I: Differentiation”, Fuzzy Sets Syst, 41(1991),269 ˆaAˇS¸284.

[6] Buckley J.J., “Fuzzy complex analysis II: Integration”, Fuzzy Sets Syst, 49(1992),171 ˆaAˇS¸179.

[7] Choi J., Datta S. K., Biswas T. and Islam N., “Some fixed point theorems in connection with two weakly compatible mappings in bicomplex valued

metric spaces”, Honam Mathematical J., 39(1)(2017),115−126.

[8] George A. and Veeramani P., “On some results in fuzzy metric spaces”, Fuzzy Sets and Systems, 64(1994),395 − 399. DOI:10.1016/0165 −

0114(94)90162−7.

[9] Grabiec M., “Fixed points in fuzzy metric spaces”, Fuzzy Sets and Systems, 27(1988),385−389. DOI:10.1016/0165−0114(88)90064−4.

[10] Ismat Beg I., Datta S.K. and Pal D., “Fixed point in bicomplex valued metric spaces”,Int. J. Nonlinear Anal. Appl., 12(2)(2021),717−727. DOI :

10.22075/i jnaa.2019.19003.2049.

[11] Kramosil I. and Michalek J., “Fuzzy metric and statistical metric spaces”, Kybernetika, 11(1975),326−334. URL: htt p : //dml.cz/dmlcz/125556.

[12] Melliani S., and Moussaoui A., “Fixed point theorem using a new class of fuzzy contractive mappings”, Journal of Universal Mathematics,

1(2)(2018),148−154.

[13] Mihet D., “Fuzzy ψ-contractive mappings in non-archimedean fuzzy metric spaces”, Fuzzy Sets and Systems, 159(6)(2008),739 − 744.

DOI:10.1016/ j. f ss.2007.07.006.

[14] Mlaiki N., Aydi H., Souayah N. and Abdeljawad T., “On Complex-Valued Triple Controlled Metric Spaces and Applications”, Journal of Function

Spaces, 2021(7)(2021),5563456. DOI : 10.1155/2021/5563456.

[15] Pal D., Rakesh Sarkar R., Manna A. and Datta S.K., “A common fixed point theorem for six mappings in bicomplex valued metric spaces”, Journal of

Xi’an University of Architecture and Technology, 13(1)(2021),168−176.

[16] Price G. B., “An Introduction to Multicomplex Spaces and Functions”, Marcel Dekker, New York, 1991.

[17] Ramot D., Milo R., Friedman M. and Kandel A.,“Complex fuzzy sets”, IEEE Transactions of Fuzzy Systems, 10(2)(2002),171−186.

[18] Segre C., “Le Rappresentazioni Reali delle Forme Complesse a Gli Enti Iperalgebrici, Math. Ann., 40(1892),413−467.

[19] Shukla S., Gopal D. and Sintunavarat W., “A new class of fuzzy contractive mappings and fixed point theorems”, Fuzzy Sets and Systems, 350(2018),85−

94. DOI:10.1016/ j. f ss.2018.02.010.

[20] Singh D., Joshi V., Imdad M. and Kumam P., “A novel framework of complex valued fuzzy metric spaces and fixed point theorems”, Journal of

Intelligent and Fuzzy Systems, 30(2016),3227−3238. DOI:10.3233/IFS−152065.

[21] Wardowski D., “Fuzzy contractive mappings and fixed points in fuzzy metric spaces”, Fuzzy Sets and Systems, 222(2013),108 − 114. DOI:

10.1016/ j. f ss.2013.01.012.

[22] Zadeh L. A., “Fuzzy sets”, Inform and Control, 8(1965),338−353. DOI:10.1016/S0019−9958(65)90241−X


How to Cite

Tiwari , R., & Rajput, S. (2024). Fixed point results in tricomplex valued fuzzy metric spaces with application. International Journal of Engineering and Technology, 13(1), 48-59. https://doi.org/10.14419/czk1y603