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Coincidence point of L-fuzzy sets endowed with graph. (English) Zbl 1425.54022

Summary: In the present paper, coincidence theorems of a crisp mapping and a sequence of \(L\)-fuzzy mappings have been produced under graphic contractive conditions in connection with notions of \(D_{\alpha_{L}}\) and \(d_{L}^{\infty}\) distances on the class of \(L\)-fuzzy sets. Further, we obtain some fixed point theorems for \(L\)-fuzzy set-valued mappings and pull out a variety of current results on fixed points for fuzzy mappings and multivalued mappings in the literature. As applications, we acquire coincidence points of a sequence of multivalued mappings with a self mapping and prove the existence of solution for fuzzy integral equations.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54A40 Fuzzy topology
54C60 Set-valued maps in general topology
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[1] Zadeh, LA, Fuzzy sets, Inform Control, 8, 338-353, (1965) · Zbl 0139.24606 · doi:10.1016/S0019-9958(65)90241-X
[2] Kramosil, I.; Michalek, J., Fuzzy metric and statistical metric spaces, Kibernetika, 11, 336-344, (1975) · Zbl 0319.54002
[3] George, A.; Veeramani, P., On some results in fuzzy metric spaces, Fuzzy Sets Syst., 64, 395-399, (1994) · Zbl 0843.54014 · doi:10.1016/0165-0114(94)90162-7
[4] Heilpern, S., Fuzzy mappings and fixed point theorems, J. Math. Anal. Appl., 83, 566-569, (1981) · Zbl 0486.54006 · doi:10.1016/0022-247X(81)90141-4
[5] Azam, A.; Beg, I., Common fixed points of fuzzy maps, Math. Comp. Model., 49, 1331-1336, (2009) · Zbl 1165.54311 · doi:10.1016/j.mcm.2008.11.011
[6] Goguen, JA, L-fuzzy sets, J. Math. Anal. Appl., 18, 145-174, (1967) · Zbl 0145.24404 · doi:10.1016/0022-247X(67)90189-8
[7] Azam, A.; Mehmood, N.; Rashid, M.; Pavlović, M., L-fuzzy fixed points in cone metric spaces, J. Adv. Math. Stud., 9, 121-131, (2016) · Zbl 1353.54032
[8] Rashid, Maliha; Azam, Akbar; Mehmood, Nayyar, L-Fuzzy Fixed Points Theorems forL-Fuzzy Mappings viaβℱL-Admissible Pair, The Scientific World Journal, 2014, 1-8, (2014)
[9] Rashid, M.; Kutbi, MA; Azam, A., Coincidence theorems via alpha cuts of L-fuzzy sets with applications, Fixed Point Theory Appl., 2014, 212, (2014) · Zbl 1375.54022 · doi:10.1186/1687-1812-2014-212
[10] Jachymski, J., The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc., 136.4, 1359-1373, (2008) · Zbl 1139.47040
[11] Azam, A.; Arshad, M., Fixed points of a sequence of locally contractive multivalued maps, Comp. Math. Appl., 57, 96-100, (2009) · Zbl 1165.47305 · doi:10.1016/j.camwa.2008.09.039
[12] Nadler, SB, Multivalued contraction mappings, Pacific J. Math., 30, 475-488, (1969) · Zbl 0187.45002 · doi:10.2140/pjm.1969.30.475
[13] Beg, I.; Azam, A., Fixed points of multivalued locally contractive mappings, Boll. Un. Mat. Ital. (4A), 7, 227-233, (1990) · Zbl 0717.54023
[14] Hu, T., Fixed point theorems for multivalued mappings, Canad. Math. Bull., 23, 193-197, (1980) · Zbl 0436.54037 · doi:10.4153/CMB-1980-026-2
[15] Du, WS, On coincidence point and fixed point theorems for nonlinear multivalued maps, Topol. Appl., 159, 49-56, (2012) · Zbl 1231.54021 · doi:10.1016/j.topol.2011.07.021
[16] Mizoguchi, N.; Takahashi, W., Fixed point theorems for multi-valued mappings on complete metric spaces, J. Math. Anal. Appl., 188, 141-177, (1989) · Zbl 0688.54028
[17] Suzuki, T., Mizoguchi-Takahashi’s fixed point theorem is a real generalization of Nadler’s, J. Math. Anal. Appl., 340, 752-755, (2008) · Zbl 1137.54026 · doi:10.1016/j.jmaa.2007.08.022
[18] Edelstein, M., An extension of Banach’s contraction principle, Proc. Amer. Math. Soc., 12, 7-12, (1961) · Zbl 0096.17101
[19] Lakshmikantham, V., Mohapatra, R.N.: Theory of fuzzy differential equations and inclusions. CRC Press, Boca Raton (2004) · Zbl 1072.34001
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