Geodesic
A natural selection of a graphic contraction transformation in fuzzy metric spaces
Alolaiyan, Hanan 1 ; Saleem, Naeem 2 ; Abbas, Mujahid 3
1 Department of Mathematics, King Saud University, Saudi Arabia
2 Department of Mathematics, University of Management and Technology, Lahore, Pakistan
3 Department of Mathematics, Government College University, Lahore, Pakistan;Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia
Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 2, p. 218-227.

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

In this paper, we study sufficient conditions to find a vertex $v$ of a graph such that $Tv$ is a terminal vertex of a path which starts from $v,$ where $T$ is a self graphic contraction transformation defined on the set of vertices. Some examples are presented to support the results proved herein. Our results widen the scope of various results in the existing literature.
DOI : 10.22436/jnsa.011.02.04
Classification : 47H10, 47H04, 47H07, 54H25, 54C60
Keywords: Graphic contraction, fuzzy metric space, natural selection

Alolaiyan, Hanan  1 ; Saleem, Naeem  2 ; Abbas, Mujahid  3

1 Department of Mathematics, King Saud University, Saudi Arabia
2 Department of Mathematics, University of Management and Technology, Lahore, Pakistan
3 Department of Mathematics, Government College University, Lahore, Pakistan;Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia 
@article{JNSA_2018_11_2_a3,
     author = {Alolaiyan, Hanan  and Saleem, Naeem  and Abbas, Mujahid },
     title = {A natural selection of a graphic contraction transformation in fuzzy metric spaces},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {218-227},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {2018},
     doi = {10.22436/jnsa.011.02.04},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.011.02.04/}
}
TY  - JOUR
AU  - Alolaiyan, Hanan 
AU  - Saleem, Naeem 
AU  - Abbas, Mujahid 
TI  - A natural selection of a graphic contraction transformation in fuzzy metric spaces
JO  - Journal of nonlinear sciences and its applications
PY  - 2018
SP  - 218
EP  - 227
VL  - 11
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.011.02.04/
DO  - 10.22436/jnsa.011.02.04
LA  - en
ID  - JNSA_2018_11_2_a3
ER  - 
%0 Journal Article
%A Alolaiyan, Hanan 
%A Saleem, Naeem 
%A Abbas, Mujahid 
%T A natural selection of a graphic contraction transformation in fuzzy metric spaces
%J Journal of nonlinear sciences and its applications
%D 2018
%P 218-227
%V 11
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.011.02.04/
%R 10.22436/jnsa.011.02.04
%G en
%F JNSA_2018_11_2_a3
Alolaiyan, Hanan ; Saleem, Naeem ; Abbas, Mujahid . A natural selection of a graphic contraction transformation in fuzzy metric spaces. Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 2, p. 218-227. doi : 10.22436/jnsa.011.02.04. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.011.02.04/

[1] Abbas, M.; T. Nazir Common fixed point of a power graphic contraction pair in partial metric spaces endowed with a graph, Fixed Point Theory Appl., Volume 2013 (2013 ), pp. 1-8 | DOI | Zbl

[2] Abbas, M.; Nazir, T.; S. Radenović Common fixed points of four maps in partially ordered metric spaces, Appl. Math. Lett., Volume 24 (2011), pp. 1520-1526 | DOI

[3] Abbas, M.; B. E. Rhoades Fixed point theorems for two new classes of multivalued mappings , Appl. Math. Lett., Volume 22 (2009), pp. 1364-1368 | Zbl | DOI

[4] A. Azam Coincidence points of mappings and relations with applications , Fixed Point Theory Appl., Volume 2012 (2012 ), pp. 1-9 | DOI | Zbl

[5] George, A.; P. Veeramani On some results in fuzzy metric spaces, Fuzzy Sets and Systems, Volume 64 (1994), pp. 395-399 | DOI

[6] George, A.; P. Veeramani On some results of analysis for fuzzy metric spaces , Fuzzy Sets and Systems, Volume 90 (1997), pp. 365-368 | DOI

[7] M. Grabiec Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, Volume 27 (1988), pp. 385-389 | DOI

[8] Gregori, V.; S. Romaguera Some properties of fuzzy metric spaces, Fuzzy Sets and Systems, Volume 115 (2000), pp. 485-489 | DOI

[9] Gregori, V.; A. Sapena On fixed-point theorems in fuzzy metric spaces , Fuzzy Sets and Systems, Volume 125 (2002), pp. 245-252 | DOI

[10] Gwozdz-Lukawska, G.; J. Jachymski IFS on a metric space with a graph structure and extensions of the Kelisky-Rivlin theorem, J. Math. Anal. Appl., Volume 356 (2009), pp. 453-463 | Zbl | DOI

[11] Hosseini, H. B.; Saadati, R.; M. Amini Alexandroff theorem in fuzzy metric spaces, Math. Sci. Res. J., Volume 8 (2004), pp. 357-361 | Zbl

[12] J. Jachymski The contraction principle for mappings on a metric space with a graph , Proc., Amer. Math. Soc., Volume 136 (2008), pp. 1359-1373

[13] Jachymski, J.; I. J Jóźwik Nonlinear contractive conditions: a comparison and related problems, Banach Center Publ., Volume 77 (2007), pp. 123-146 | Zbl | DOI

[14] Kramosil, I.; Michálek, J. Fuzzy metric and statistical metric spaces, Kybernetika, Volume 11 (1975), pp. 336-344

[15] Nieto, J. J.; Pouso, R. L.; R. Rodríguez-López Fixed point theorems in ordered abstract spaces , Proc. Amer. Math. Soc., Volume 135 (2007), pp. 2505-2517 | DOI

[16] Ran, A. C. M.; Reurings, M. C. B. A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., Volume 132 (2004), pp. 1435-1443 | Zbl | DOI

[17] Rodríguez-López, J.; S. Romaguera The Hausdorff fuzzy metric on compact sets , Fuzzy Sets and Systems, Volume 147 (2004), pp. 273-283 | DOI

[18] Saleem, N.; Ali, B.; Abbas, M.; Z. Raza Fixed points of Suzuki type generalized multivalued mappings in fuzzy metric spaces with applications , Fixed Point Theory Appl., Volume 2015 (2015), pp. 1-18 | Zbl | DOI

[19] Schweizer, B.; A. Sklar Statistical metric spaces , Pacific J. Math., Volume 10 (1960), pp. 314-334

[20] L. A. Zadeh Fuzzy Sets, Informations and control, Volume 8 (1965), pp. 338-353

Cité par Sources :