Geodesic
Fixed points of fuzzy multivalued $F$-contractive mappings with a directed graph in parametric metric spaces
Problemy analiza, Tome 13 (2024) no. 3, pp. 79-100 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the structure of a parametric metric space accompanied by directed graph, we introduce the idea of fuzzy multivalued $F$-contractive mappings. Results related to the existence of common fuzzy fixed points are introduced. The proved results are supported by an example. Our results bring together, sum up, and supplement different familiar related results in the literature. We hope that the acclaimed results in our work will encourage new analysis aspects in fixed-point theory and parallel hybrid models in the literature of fuzzy mathematics supplemented with a graph.
Keywords: $F$-contraction, fuzzy set, fuzzy multivalued mapping, fuzzy fixed point. 
@article{PA_2024_13_3_a5,
     author = {M. Rafique and T. Nazir and H. Kalita},
     title = {Fixed points of fuzzy multivalued $F$-contractive mappings with a directed graph in parametric metric spaces},
     journal = {Problemy analiza},
     pages = {79--100},
     year = {2024},
     volume = {13},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2024_13_3_a5/}
}
TY  - JOUR
AU  - M. Rafique
AU  - T. Nazir
AU  - H. Kalita
TI  - Fixed points of fuzzy multivalued $F$-contractive mappings with a directed graph in parametric metric spaces
JO  - Problemy analiza
PY  - 2024
SP  - 79
EP  - 100
VL  - 13
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/PA_2024_13_3_a5/
LA  - en
ID  - PA_2024_13_3_a5
ER  - 
%0 Journal Article
%A M. Rafique
%A T. Nazir
%A H. Kalita
%T Fixed points of fuzzy multivalued $F$-contractive mappings with a directed graph in parametric metric spaces
%J Problemy analiza
%D 2024
%P 79-100
%V 13
%N 3
%U http://geodesic.mathdoc.fr/item/PA_2024_13_3_a5/
%G en
%F PA_2024_13_3_a5
M. Rafique; T. Nazir; H. Kalita. Fixed points of fuzzy multivalued $F$-contractive mappings with a directed graph in parametric metric spaces. Problemy analiza, Tome 13 (2024) no. 3, pp. 79-100. http://geodesic.mathdoc.fr/item/PA_2024_13_3_a5/

[1] Abbas M., Ali B., Romaguera S., “Fixed and periodic points of generalized contractions in metric spaces”, Fixed Point Theory Appl., 243 (2013), 1–11 | DOI | MR

[2] Abbas M., Alfuraidan M. R., Nazir T., “Common fixed points of multivalued F-contractions on metric spaces with a directed graph”, Carpathian J. Math., 32 (2016), 1–12 | DOI | MR | Zbl

[3] Abbas M., Nazir T., “Common fixed point of a power graphic contraction pair in partial metric spaces endowed with a graph”, Fixed Point Theory Appl., 20 (2013), 01–08 | DOI | MR

[4] Abbas M., Rhoades B. E., “Fixed point theorems for two new classes of multi-valued mappings”, Appl. Math. Lett., 22 (2009), 1364–1368 | DOI | MR | Zbl

[5] Acar O., Durmaz G., Minak G., “Generalized multi-valued F-contractions on complete metric spaces”, Bulletin Iran. Math. Soc., 40 (2014), 1469–1478 | MR | Zbl

[6] Al-Mazrooei A. E., Ahmad J., “Fixed point theorems for fuzzy mappings with applications”, J. Intell. Fuzzy Syst., 36 (2019), 3903–3909 | DOI | MR

[7] Atanassov K. T., Intuitionistic fuzzy sets, Physica, 35, Heidelberg, 1999, 1–137 | DOI | MR

[8] Azam A., Arshad M., Vetro P., “On a pair of fuzzy $ \varphi $-contractive mappings”, Math. Comput. Modelling, 52 (2010), 207–214 | DOI | MR | Zbl

[9] Azam A., Beg I., “Common fixed points of fuzzy maps”, Math. Comput. Modelling, 49 (2009), 1331–1336 | DOI | MR | Zbl

[10] Berinde V., “Approximating fixed points of weak contractions using the Picard iteration”, Nonlinear Anal. Forum, 9 (2004), 43–53 | MR | Zbl

[11] Berinde M., Berinde V., “On a general class of multivalued weakly Picard mappings”, J. Math. Anal. Appl., 326 (2007), 772–782 | DOI | MR | Zbl

[12] Bose R. K., Sahani D., “Fuzzy mappings and fixed point theorems”, Fuzzy Sets and Systems, 21 (1987), 53–58 | DOI | MR | Zbl

[13] Goguen J. A., “L-fuzzy sets”, J. Math. Anal. Appl., 18 (1967), 145–174 | DOI | MR | Zbl

[14] Heilpern S., “Fuzzy mappings and fixed point theorem”, J. Math. Anal. Appl., 83 (1981), 566–569 | DOI | MR | Zbl

[15] Hussain N., Salimi P., Parvaneh V., “Fixed point results for various contractions in parametric and fuzzy b-metric spaces”, J. Nonlinear Sci. Appl., 8:5 (2015), 719–739 | DOI | MR | Zbl

[16] Shagari M. S., “On fuzzy soft set-valued maps with application”, J. Nig. Soc. Phys. Sci., 2 (2020), 26–35 | DOI | MR

[17] Shagari M. S., Azam A., “Fixed point theorems of fuzzy set-valued maps with applications”, Probl. Anal.-Issues Anal., 9 (2020), 68–86 | DOI | MR | Zbl

[18] Shagari M. S., Azam A., “Fixed points of soft-set valued and fuzzy set-valued maps with applications”, J. Intell. Fuzzy Syst., 37 (2019), 3865–3877 | DOI | MR

[19] Jachymski J., “The contraction principle for mappings on a metric space with a graph”, Proc. Amer. Math. Soc., 136 (2008), 1359–1373 | DOI | MR | Zbl

[20] Jachymski J., Jozwik I., “Nonlinear contractive conditions: a comparison and related problems”, Banach Center Publ., 77, 2007, 123–146 | DOI | MR | Zbl

[21] Kannan R., “Some results on fixed points”, Bull. Calcutta. Math. Soc., 60 (1968), 71–76 | DOI | MR | Zbl

[22] Latif A., Beg I., “Geometric fixed points for single and multivalued mappings”, Demonstratio Math., 30 (1997), 791–800 | DOI | MR | Zbl

[23] Markin J. T., “Continuous dependence of fixed point sets”, Proc. Amer. Math. Soc., 38 (1973), 545–547 | DOI | MR | Zbl

[24] Nadler S.B., “Multi-valued contraction mappings”, Pacific J. Math., 30 (1969), 475–488 | DOI | MR | Zbl

[25] Nieto J. J., Lopez R. R., “Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations”, Order, 22 (2005), 223–239 | DOI | MR | Zbl

[26] Qiu D., Shu L., “Supremum metric on the space of fuzzy sets and common fixed point theorems for fuzzy mappings”, Information Sciences, 178 (2008), 3595–3604 | DOI | MR | Zbl

[27] Ran A. C. M., Reurings M. C. B., “A fixed point theorem in partially ordered sets and some application to matrix equations”, Proc. Amer. Math. Soc., 132 (2004), 1435–1443 | DOI | MR | Zbl

[28] Rus I. A., Petrusel A., Sintamarian A., “Data dependence of fixed point set of some multivalued weakly Picard operators”, Nonlinear Anal., 52:8 (2003), 1944–1959 | DOI | MR

[29] Sgroi M., Vetro C., “Multi-valued F-contractions and the solution of certain functional and integral equations”, Filomat, 27:7 (2013), 1259–1268 | DOI | MR | Zbl

[30] Wardowski D., “Fixed points of new type of contractive mappings in complete metric spaces”, Fixed Point Theory Appl., 94 (2012), 01–06 | DOI | MR

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