Fixed point theorems of fuzzy set-valued maps with applications
Problemy analiza, Tome 9 (2020) no. 2, pp. 68-86.

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In this paper, we introduce the notion of Suzuki-type $(\alpha, \beta)$-weak contractions in the setting of fuzzy set-valued maps, thereby establishing some fuzzy fixed point theorems. Moreover, one of our theorems is applied to study a homotopy result.
Keywords: fuzzy set, fuzzy set-valued mapping, fixed point, weak contraction.
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Mohammed Shehu Shagari; Akbar Azam. Fixed point theorems of fuzzy set-valued maps with applications. Problemy analiza, Tome 9 (2020) no. 2, pp. 68-86. http://geodesic.mathdoc.fr/item/PA_2020_9_2_a4/

[1] Azam A., Arshad M., Vetro P., “On a pair of fuzzy $\varphi$-contractive mappings”, Mathematical and Computer Modelling, 52:1-2 (2010), 207–214 | DOI | MR | Zbl

[2] Azam A., Beg I., “Common fixed points of fuzzy maps”, Mathematical and computer modelling, 49:7 (2009), 1331–1336 | DOI | MR | Zbl

[3] Azam A., Arshad M., Beg I., “Fixed points of fuzzy contractive and fuzzy locally contractive maps”, Chaos, Solitons and Fractals, 42:5 (2009), 2836–2841 | DOI | MR | Zbl

[4] Banach S., “Sur les operations dans les ensembles abstraits et leur application aux equations integrales”, Fund. math., 3:1 (1922), 133–181 | DOI | MR | Zbl

[5] Berinde V., “Approximating fixed points of weak contractions using the Picard iteration”, Nonlinear Analysis Forum, 9 (2004), 43–54 | MR

[6] Butnariu D., “Fixed points for fuzzy mappings”, Fuzzy sets and Systems, 7:2 (1982), 191–207 | DOI | MR | Zbl

[7] Chatterjea S.K., “Fixed point theorems”, C.R. Acad. Bulgare Sci., 25 (1972), 727–730 | MR | Zbl

[8] Ciric L. B., “Fixed points for generalized multi-valued contractions”, Math. Vesnik, 9:24 (1972), 265–272 | MR | Zbl

[9] Doric D., Lazovic R., “Some Suzuki-type fixed point theorems for generalized multivalued mappings and applications”, Fixed Point Theory and Applications, 40:1 (2011) | DOI | MR

[10] Edelstein M., “On fixed and periodic points under contractive mappings”, Journal of the London Mathematical Society, 1:1 (1962), 74–79 | DOI | MR

[11] Heilpern S., “Fuzzy mappings and fixed point theorem”, Journal of Mathematical Analysis and Applications, 83:2 (1981), 566–569 | DOI | MR | Zbl

[12] Humaira M. S., Tunc C., “Fuzzy fixed point results via rational type contractions involving control functions in complex-valued metric spaces”, Appl. Math., 12:4 (2018), 861–875 | MR

[13] Kannan R., “Some results on fixed points II”, The American Mathematical Monthly, 76:4 (1969), 405–408 | MR | Zbl

[14] Rome B. E., Sarwar M., Kumam P., “Fixed point theorems via $\alpha-\varrho-$fuzzy contraction”, Axioms, 8:2 (2019), 69 | DOI | Zbl

[15] Mohammed S. S., “On bilateral fuzzy contractions”, Functional Analysis, Approximation and Computation, 12:1 (2020), 1–13 | MR | Zbl

[16] Sarwar M., Kishore G. N. V., “Fuzzy fixed point results for contractive mapping with applications”, Complexity, 2018 | MR

[17] Sarwar M., Kumam P., “Common fixed point results for fuzzy mappings on complex-valued metric spaces with homotopy results”, Symmetry, 11:1 (2019), 61 | DOI | Zbl

[18] Sarwar M., Li T., “Fuzzy fixed point results and applications to ordinary fuzzy differential equations in complex valued metric spaces”, Hacettepe Journal of Mathematics and Statistics, 48:6 (2019), 1712–1728 | MR

[19] Suzuki T., “A generalized Banach contraction principle that characterizes metric completeness”, Proceedings of the American Mathematical Society, 136:5 (2008), 1861–1869 | DOI | MR | Zbl

[20] Weiss M. D., “Fixed points, separation, and induced topologies for fuzzy sets”, Journal of Mathematical Analysis and Applications, 50:1 (1975), 142–150 | DOI | MR | Zbl

[21] Zadeh L. A., “Fuzzy sets”, Information and control, 8:3 (1965), 338–353 | DOI | MR | Zbl

[22] Zamfirescu T., “Fixed point theorems in metric spaces”, Archiv der Mathematik, 23:1 (1972), 292–298 | DOI | MR | Zbl