Fixed points for a sequence of $\mathcal{L}$-fuzzy mappings in non-Archimedean ordered modified intuitionistic fuzzy metric spaces
Journal of nonlinear sciences and its applications, Tome 14 (2021) no. 2, p. 97-108.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper, we obtain sufficient conditions for the existence of fixed points for a sequence of $\mathcal{L}$-fuzzy mappings in a non-Archimedean ordered modified intuitionistic fuzzy metric space. We use contractive conditions of implicit relation. Further, as an application, we also generalize our usual contractive conditions into integral contractive conditions.
DOI : 10.22436/jnsa.014.02.05
Classification : 47H10, 54H25
Keywords: Ordered modified intuitionistic fuzzy metric, \(\mathcal{L}\)-fuzzy mappings, fixed points

Ahmed, M. A.  1 ; Beg, Ismat  2 ; Khafagy, S. A.  3 ; Nafadi, H. A.  4

1 Department of Mathematics, Faculty of Science, Al-Zulfi, Majmaah University, Majmaah 11952, Saudi Arabia;Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt
2 Centre for Mathematics and Statistical Sciences, Lahore School of Economics, Lahore 53200, Pakistan
3 Department of Mathematics, Faculty of Science, Al-Zulfi, Majmaah University, Majmaah 11952, Saudi Arabia;Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt
4 Department of Mathematics, Deanship of Preparatory Programs, Al-Imam Muhammad Ibn Saud Islamic University, Riyadh, Saudi Arabia
@article{JNSA_2021_14_2_a4,
     author = {Ahmed, M. A.  and Beg, Ismat  and Khafagy, S. A.  and Nafadi, H. A. },
     title = {Fixed points for a sequence of {\(\mathcal{L}\)-fuzzy} mappings in {non-Archimedean} ordered modified intuitionistic fuzzy metric spaces},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {97-108},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2021},
     doi = {10.22436/jnsa.014.02.05},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.014.02.05/}
}
TY  - JOUR
AU  - Ahmed, M. A. 
AU  - Beg, Ismat 
AU  - Khafagy, S. A. 
AU  - Nafadi, H. A. 
TI  - Fixed points for a sequence of \(\mathcal{L}\)-fuzzy mappings in non-Archimedean ordered modified intuitionistic fuzzy metric spaces
JO  - Journal of nonlinear sciences and its applications
PY  - 2021
SP  - 97
EP  - 108
VL  - 14
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.014.02.05/
DO  - 10.22436/jnsa.014.02.05
LA  - en
ID  - JNSA_2021_14_2_a4
ER  - 
%0 Journal Article
%A Ahmed, M. A. 
%A Beg, Ismat 
%A Khafagy, S. A. 
%A Nafadi, H. A. 
%T Fixed points for a sequence of \(\mathcal{L}\)-fuzzy mappings in non-Archimedean ordered modified intuitionistic fuzzy metric spaces
%J Journal of nonlinear sciences and its applications
%D 2021
%P 97-108
%V 14
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.014.02.05/
%R 10.22436/jnsa.014.02.05
%G en
%F JNSA_2021_14_2_a4
Ahmed, M. A. ; Beg, Ismat ; Khafagy, S. A. ; Nafadi, H. A. . Fixed points for a sequence of \(\mathcal{L}\)-fuzzy mappings in non-Archimedean ordered modified intuitionistic fuzzy metric spaces. Journal of nonlinear sciences and its applications, Tome 14 (2021) no. 2, p. 97-108. doi : 10.22436/jnsa.014.02.05. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.014.02.05/

[1] Ahmed, M. A.; Nafadi, H. A. Common fixed point theorems for hybrid pairs of maps in fuzzy metric spaces, J. Egyptian Math. Soc., Volume 22 (2014), pp. 453-458 | DOI | Zbl

[2] Ali, J.; Ahmed, M. A.; Nafadi, H. A. Common fixed points for $L$-fuzzy mappings in $b$-metric spaces, J. Appl. Math. Inform., Volume 35 (2017), pp. 231-239 | DOI

[3] Beg, I.; Ahmed, M. A.; Nafadi, H. A. Fixed points for $L$-fuzzy mappings in ordered $b$-metric spaces, J. Func. Spaces, Volume 2018 (2018), pp. 1-9

[4] Beg, I.; Ahmed, M. A.; Nafadi, H. A. (JCLR) property and fixed point in non-Archimedean fuzzy metric spaces, Int. J. Nonlinear Anal. Appl., Volume 9 (2018), pp. 195-201

[5] Beg, I.; Butt, A. R. Common fixed point and coincidence point of generalized contractions in ordered metric spaces, Fixed Point Theory Appl., Volume 2012 (2012), pp. 1-12 | Zbl | DOI

[6] Beloul, S.; Tomar, A. Integral type common fixed point theorems inmodified intuitionistic fuzzy metric spaces, Afrika Matematika, Volume 30 (2019), pp. 581-596

[7] Branciari, A. A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci., Volume 29 (2002), pp. 531-536 | DOI | Zbl

[8] Deschrijver, G.; Cornelis, C.; Kerre, E. E. On the representation of intuitionistic fuzzy $t$-norms and $t$-conorms, IEEE Trans Fuzzy Syst., Volume 12 (2004), pp. 45-61

[9] Deschrijver, G.; Kerre, E. E. On the relationship between some extensions of fuzzy set theory, Fuzzy Sets and Systems, Volume 133 (2003), pp. 227-235

[10] Geobel, K.; Kirk, W. A. Topics in metric fixed point theory, Cambridge University Press, Cambridge, 1990 | Zbl

[11] Goguen, J. A. $L$-fuzzy sets, J. Math. Anal. Appl., Volume 18 (1967), pp. 145-174 | DOI | Zbl

[12] Gregori, V.; Romaguera, S.; Veereamani, P. A note on intuitionistic fuzzy metric spaces, Chaos Solitons Fractals, Volume 28 (2006), pp. 902-905 | DOI | Zbl

[13] Hadžić, O.; Pap, E. Fixed Point Theory in Probabilistic Metric Spaces, Kluwer Academic Publishers, Dordrecht, 2001

[14] Imdad, M.; Ahmed, M. A.; Nafadi, H. A. Common fixed point theorems for hybrid pairs of $L$-fuzzy mappings in non-Archimedean modified intuitionistic fuzzy metric spaces, J. Int. Fuzzy. Syst., Volume 33 (2017), pp. 667-677 | DOI | Zbl

[15] Imdad, M.; Ahmed, M. A.; Nafadi, H. A.; Sharma, A. Fixed point theorems for $L$-fuzzy mappings in $L$-fuzzy metric spaces, J. Int. Fuzzy. Syst., Volume 35 (2018), pp. 683-692

[16] Kirk, W.; Shahzad, N. Fixed point theory in distance spaces, Springer, Cham, 2014 | DOI | Zbl

[17] Park, J. H. Intuitionistic fuzzy metric spaces, Chaos Solitons Fractals, Volume 22 (2004), pp. 1039-1046 | Zbl | DOI

[18] Rao, K. P. R.; Altun, I.; Rao, K. R. K.; Srinivasarao, N. A common fixed point theorem for four maps under $\psi$-$\phi$ contractive condition of integral type in ordered partial metric spaces, Math. Sci. Lett., Volume 4 (2015), pp. 25-31

[19] Rashid, M.; Azam, A.; Mehmood, N. $L$-Fuzzy Fixed Points Theorems for $L$-Fuzzy Mappings via $B-{\Im_{L}}$-Admissible Pair, Sci. World J., Volume 2014 (2014), pp. 1-8

[20] Saadati, R.; Sedghi, S.; Shobe, N. Modified intuitionistic fuzzy metric spaces and some fixed point theorems, Chaos Solitons Fractals, Volume 38 (2008), pp. 36-47 | DOI | Zbl

[21] Saadati, R.; Vaezpour, S. M.; Cho, Y. J. Quicksort algorithm: Application of a fixed point theorem in intuitionistic fuzzy quasi-metric spaces at a domain of words, J. Comput. Appl. Math., Volume 228 (2009), pp. 219-225 | Zbl | DOI

[22] Saini, R. K.; Sharma, A. Common fixed point result of multivalued and singlevalued mappings in partially ordered metric space, Adv. Pure Math., Volume 3 (2013), pp. 142-148

[23] Zadeh, L. A. Fuzzy set, Information and Control, Volume 8 (1965), pp. 338-353 | DOI

Cité par Sources :