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Articles

Existence and Uniqueness of a Common Best Proximity Point on Fuzzy Metric Space

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Pages 54-63 | Received 09 Dec 2019, Accepted 08 Mar 2020, Published online: 10 Jul 2020

References

  • Sessa S. On a weak commutativity condition in fixed point considerations. Publ Inst Math (Belgr). 1982;34(46):149–153.
  • Jungck G. Compatible mappings and common fixed points. Int J Math Math Sci. 1986;9(4):771–779. doi: 10.1155/S0161171286000935
  • Jungck G, Rhoades BE. Fixed points for set valued functions without continuity. Indian J Pure Appl Math. 1998;29(3):227–238.
  • Abkar A, Gabeleh M. Best proximity points for cyclic mappings in ordered metric spaces. J Optim Theory Appl. 2011;150(1):188–193. doi: 10.1007/s10957-011-9810-x
  • Abkar A, Gabeleh M. Generalized cyclic contractions in partially ordered metric spaces. Optim Lett. 2011;6:1819–1830. doi: 10.1007/s11590-011-0379-y
  • Al-Thagafi MA, Shahzad N. Convergence and existence results for best proximity points. Nonlinear Anal. 2009;70:3665–3671. doi: 10.1016/j.na.2008.07.022
  • Eldred A A, Veeramani P. Existence and convergence of best proximity points. J Math Anal Appl. 2006;323:1001–1006. doi: 10.1016/j.jmaa.2005.10.081
  • Zadeh LA. Fuzzy sets. Inform and Comput. 1965;8:338–353.
  • George A, Veeramani P. On some results in fuzzy metric spaces. Fuzzy Sets Syst. 1994;64(3):395–399. doi: 10.1016/0165-0114(94)90162-7
  • Fang J X. Common fixed point theorems of compatible and weakly compatible maps in Menger spaces. Nonlinear Anal. 2009;71:1833–1843. doi: 10.1016/j.na.2009.01.018
  • Hu XQ. Common coupled fixed point theorems for contractive mappings in fuzzy metric spaces. Fixed Point Theory Appl. 2011;2011(1):363–716.
  • Sedghi S, Altun I, Shobe N, et al. Coupled fixed point theorems for contractions in fuzzy metric spaces. Nonlinear Anal. 2010;72:1298–1304. doi: 10.1016/j.na.2009.08.018
  • Aamri M, El Moutawakil D. Some new common fixed point theorems under strict contractive conditions. J Math Anal Appl. 2002;270(1):181–188. doi: 10.1016/S0022-247X(02)00059-8
  • Sintunavarat W, Kumam P. Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces. J Appl Math. 2011;2011(14). Article ID 637958.
  • Jain M, Tas K, Kumar S, et al. Coupled fixed point theorems for a pair of weakly compatible maps along with CLRg property in fuzzy metric spaces. J Appl Math. 2012;2012(13). Article ID 961210.
  • Roldán-López-de-Hierro AF, Sintunavarat W. Common fixed point theorems in fuzzy metric spaces using the CLRg property. Fuzzy Sets Syst. 2016;282:131–142. doi: 10.1016/j.fss.2014.11.005
  • Saha P, Guria S, Choudhury BS, et al. Determining fuzzy distance through non-self fuzzy contractions. Yugosl J Oper Res. 2019. https://doi.org/10.2298/YJOR180515002S.
  • Shayanpour H, Nematizadeh A. Some results on common best proximity point in fuzzy metric spaces. Bol Soc Parana Mat. 2017;35:177–194. doi: 10.5269/bspm.v35i2.29466
  • Vetro C, Salimi P. Best proximity point results in non-Archimedean fuzzy metric spaces. Fuzzy Inf Eng. 2013;5(4):417–429. doi: 10.1007/s12543-013-0155-z
  • Abbas M, Saleem N, De la Sen M, et al. Optimal coincidence point results in partially ordered non-Archimedean fuzzy metric spaces. Fixed Point Theory Appl. 2016;2016(1):44. doi: 10.1186/s13663-016-0534-3
  • Zhu X-H, Xiao J-Z. Note on “coupled fixed point theorems for contractions in fuzzy metric spaces”. Nonlinear Anal. 2011;74:5475–5479. doi: 10.1016/j.na.2011.05.034