In this paper, the notion of soft set-valued mappings and E-soft fixed points are introduced. These ideas are used to establish some analogues of classical fixed point theorems in the literature. Some Examples are given to support the hypotheses of the theorems. A few graphical and tabular illustrations are also provided so as to visualize the novel concepts pictorially. Moreover, as an application of one of the presented results, an existence condition for a solution of nonlinear discrete-type delay differential equation is provided.
AlcantudJ.C.R., A novel algorithm for fuzzy soft sets based decision making problems, J Comput Appl Math203 (2007), 412–418.
2.
AliM.I., FengF., LiuX. and ShabirM., On some new operations in soft set theory, Comput Math Appl57(9) (2009), 1547–1553.
3.
AtanassovK.T., Intuitionistic fuzzy sets, Fuzzy Sets and Systems20(1) (1986), 87–96.
4.
AzamA. and BegI., Fixed points of fuzzy contractive and fuzzy locally contractive maps, Chaos, Solitons and Fractals42 (2009), 2836–2841.
5.
AzamA., TabassumR. and RashidM., Coincidence and fixed point theorems of intuitionistic fuzzy mappings with applications, Journal of Mathematical Analysis8(4) (2017), 56–77.
6.
AzamA., Fuzzy fixed points of fuzzy mappings via a rational inequality, Journal of Mathematics and Statistics40(3) (2011), 421–431.
7.
AzamA. and RashidM., A note on fixed point theorems for fuzzy mappings by P. Vijayaraju and Marudai, Fuzzy Sets and Systems161(9) (2010), 1145–1149.
8.
AzamA. and RashidM., A fuzzy coincidence theorem with applications in function space, Journal of Intelligent and Fuzzy Systems27(4) (2014), 1775–1781.
BaileyD.F., Some theorems on contractive mappings, J Lond Math Soc41 (1966), 101–106.
11.
BanachS., Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund Math3(1) (1922), 133–181.
12.
BegI., Random edelstein theorem, Bull Greek Math Soc45 (2001), 31–41.
13.
ChenS., TsangE.C.C. and YeungS.S., The parametrization reduction of soft sets and its application, Comp Math Appl449 (2005), 757–763.
14.
ChenM.P. and ShinM.H., Fixed point theorems for point-to-point and point-to-set maps, J Math Anal Appl51 (1979), 5–524.
15.
CiricL., Some new results for Banach contraction and Edelstein conttractive mappings on fuzzy metric spaces, Chaos, Solitons and Fractals, 42, 2009, pp. 145–154.
16.
DuboisS., PradeH. and PawlakZ., Rough sets: Theoretical Aspects of Reasoning about Data, Kluwer, Dordrecht, Netherlands, 1991.
17.
EdelsteinM., On fixed and periodic points under contractive mappings, J London Math Soc37 (1962), 74–79.
18.
EdelsteinM., An extension of Banach’s contraction principle, Proc Amer Math Soc12 (1961), 7–10.
19.
FengF., LiC., DavvazB. and AliM.I., Soft sets combined with fuzzy sets and rough sets: A tentative approach, Soft Comput14(9) (2010), 899–911.
20.
FengF. and LiY.M., Soft subsets and soft product operations, Inf Sci232 (2013), 44–57.
21.
FengF., JunY. and LiX., An adjustable approach to fuzzy soft set based decision making, J Comput Appl Math234 (2010), 10–20.
22.
GorzalzanyM.B., A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy Sets and Systems21 (1987), 1–17.
23.
GuptaV., SainiR.K., ManiN. and TripathiA.K., Fixed point theorems by using control function in fuzzy metric spaces, Cogent Mathematics2(1) (2015), 1–7.
24.
HeilpernS., Fuzzy mappings and fixed point theorems, Journal of Mathematical Analysis and Applications83(2) (1981), 566–569.
25.
HuT. and RosenH., Locally contractive and expansive mappings, Proc Am Math Soc86 (1982), 656–662.
26.
KongZ., GaoL. and Wang.L., Comment on ‘A fuzzy soft theoretic approach to decision making problems’, J Comput Appl Math223 (2009), 540–542.
27.
LiuY., QinK. and MartinezL., Improving decision making approaches based on fuzzy soft sets and rough sets, Appl Soft Comput65 (2018), 320–332.
28.
LiuZ., QinK. and PeiZ., A method for fuzzy soft sets in decision making based on ideal solution, Symmetry9 (2017), 246.
29.
MaX., LiuQ. and ZhanJ., A survey of decision making methods based on certain hybrid soft models, Artif Intell Rev47 (2017), 507–530.
30.
MolodtsovS., Soft set theory, Computers Math Appl37(4) (1999), 19–31.
PengJ.H., KwunY.C. and SonM.J., A generalized intuitionistic fuzzy soft set theoretic approach to decision making problems, Int J Fuzzy Log Intell Syst11 (2011), 71–76.
36.
PawlakZ., Rough sets, Int J Inform Comput Sci11 (1982), 341–356.
37.
PawlakZ. and SkowronA., Rudiments of rough sets, Fuzzy Sets Syst17 (1985), 99–102.
38.
PedryczW., HanL., PetersJ.F., RammanaS. and ZhaiR., Caliberation of software quality, Fuzzy neural computing approachs, Neurocomputing36(1-4) (2001), 149–170.
39.
PetersJ.F., SurajZ., ShanS., RammanaS., PedryczW. and PizziN.J., Classification of meteorological volumetric radar data using rough set methods, Pattern recog, Lett24(6) (2003), 911–920.
40.
PhiangsungnoenS., SintunavaratW. and KumamP., Fuzzy fixed point theorems for fuzzy mappings via β-admissible with applications.
41.
PradeH. and DuboisS., Fuzzy sets and systems theory and applications, Academic Press, London, 1980.
42.
RosenholtzI., Evidence of a conspiracy among fixed point theorems, Proc Am Math53 (1975), 213–218.
43.
SametB., VetroC. and VetroP., Fixed point theorems for α contractive type mappings, Nonlinear Anal75 (2012), 2154–2165.
44.
ShatanawiW., Fixed and common fixed point theorems in frame of quasi metric spaces under contraction condition based on ultra distance functions, Nonlinear Analysis: Modeling and Control23(5) (2018), 724–748.
45.
ShatanawiW., Common fixed points for mappings under contractive conditions of (α; β, ψ) -Admissibility Type, Mathematics6(11) (2018), 261.
46.
SmithH., An introduction to delay differential equations with applications to the life sciences, Springer, 2010.
47.
RoyA.R. and MajiP.K., A fuzyy soft theoretic approach to decision making problems, Journal of Computational and Applied Mathematics203 (2007), 412–418.
48.
ZimmermanH.J., Fuzzy Set Theory and its Applications, Kluwer Academic Publishers, Boston, 1991.
49.
ZadehL., Fuzzy sets, Information and Control8 (1965), 338–353.
