Geodesic
Common fixed point results for multi-valued mappings with some examples
Abdou, Afrah Ahmad Noan1
1 Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia
Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 3, p. 787-798.

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

In this paper, we define the concepts of the (CLR)-property and the (owc)-property for two single-valued mappings and two multi-valued mappings in metric spaces and give some new common fixed point results for these mappings. Also, we give some examples to illustrate the main results in this paper. Our main results extend and improve some results given by some authors.
DOI : 10.22436/jnsa.009.03.07
Classification : 47H09, 46B20, 47H10, 47E10
Keywords: Weakly compatible mappings, fixed point, coincidence point, the (CLR)-property, the (owc)-property, the (CLRf )-property.

Abdou, Afrah Ahmad Noan 1

1 Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia 
@article{JNSA_2016_9_3_a6,
     author = {Abdou, Afrah Ahmad Noan},
     title = {Common fixed point results for multi-valued mappings with some examples},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {787-798},
     publisher = {mathdoc},
     volume = {9},
     number = {3},
     year = {2016},
     doi = {10.22436/jnsa.009.03.07},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.03.07/}
}
TY  - JOUR
AU  - Abdou, Afrah Ahmad Noan
TI  - Common fixed point results for multi-valued mappings with some examples
JO  - Journal of nonlinear sciences and its applications
PY  - 2016
SP  - 787
EP  - 798
VL  - 9
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.03.07/
DO  - 10.22436/jnsa.009.03.07
LA  - en
ID  - JNSA_2016_9_3_a6
ER  - 
%0 Journal Article
%A Abdou, Afrah Ahmad Noan
%T Common fixed point results for multi-valued mappings with some examples
%J Journal of nonlinear sciences and its applications
%D 2016
%P 787-798
%V 9
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.03.07/
%R 10.22436/jnsa.009.03.07
%G en
%F JNSA_2016_9_3_a6
Abdou, Afrah Ahmad Noan. Common fixed point results for multi-valued mappings with some examples. Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 3, p. 787-798. doi : 10.22436/jnsa.009.03.07. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.03.07/

[1] Aamri, M.; Moutawakil, D. El Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl., Volume 270 (2002), pp. 181-188

[2] Abbas, M.; Rhoades, B. E. Common fixed point theorems for hybrid pairs of occasionally weakly compatible mappings satisfying generalized contractive condition of integral type , Fixed Point Theory Appl., Volume 2007 (2007), pp. 1-9

[3] Aliouche, A.; Popa, V. General common fixed point theorems for occasionally weakly compatible hybrid mappings and applications, Novi Sad J. Math., Volume 39 (2009), pp. 89-109

[4] Banach, S. Sur les operations dans les ensembles abstrits et leur applications aux equations integrales, Fund. Math., Volume 3 (1992), pp. 133-181

[5] Chaipunya, P.; Mongkolkeha, C.; Sintunavarat, W.; Kumam, P. Fixed-point theorems for multivalued mappings in modular metric spaces, Abstr. Appl. Anal., Volume 2012 (2012), pp. 1-14

[6] Chang, C. C. On a fixed point theorem of contractive type, Comment. Math. Univ. St. Paul., Volume 32 (1983), pp. 15-19

[7] Chang, S. S. A common fixed point theorem for commuting mappings, Proc. Amer. Math. Soc., Volume 83 (1981), pp. 645-652

[8] Chauhan, S.; Sintunavarat, W.; Kumam, P. Common fixed point theorems for weakly compatible mappings in fuzzy metric spaces using the (JCLR)-property, Appl. Math., Volume 3 (2012), pp. 976-982

[9] Cho, Y. J.; Pathak, H. K.; Kang, S. M.; Jung, J. S. Common fixed points of compatible maps of type (\(\beta\) ) on fuzzy metric spaces, Fuzzy Sets and Systems, Volume 93 (1998), pp. 99-111

[10] Cho, Y. J.; Sharma, B. K.; Sahu, D. R. Semi-compatibility and fixed points, Math. Japon., Volume 42 (1995), pp. 91-98

[11] Das, G.; Dabata, J. P. A note on fixed points of commuting mappings of contractive type, Indian J. Math., Volume 27 (1985), pp. 49-51

[12] Das, K. M.; Naik, K. V. Common fixed-point theorems for commuting maps on a metric space, Proc. Amer. Math. Soc., Volume 77 (1979), pp. 369-373

[13] Eldred, A. A.; Anuradha, J.; Veeramani, P. On equivalence of generalized multi-valued contractions and Nadler's fixed point theorem, J. Math. Anal. Appl., Volume 336 (2007), pp. 751-757

[14] Gordji, M. Eshaghi; Baghani, H.; Khodaei, H.; Ramezani, M. A generalization of Nadler's fixed point theorem, J. Nonlinear Sci. Appl., Volume 3 (2010), pp. 148-151

[15] B. Fisher Common fixed points of four mappings, Bull. Inst. Math. Acad. Sinica, Volume 11 (1983), pp. 103-113

[16] Fisher, B. A common fixed point theorem for four mappings on a compact metric space, Bull. Inst. Math. Acad. Sinica, Volume 12 (1984), pp. 249-252

[17] Imdad, M.; M. A. Ahmed Some common fixed point theorems for hybrid pairs of maps without the completeness assumption, Math. Slovaca, Volume 62 (2012), pp. 301-314

[18] Jungck, G. Commuting mappings and fixed points, Amer. Math. Monthly, Volume 83 (1976), pp. 261-263

[19] Jungck, G. Periodic and fixed points, and commuting mappings, Proc. Amer. Math. Soc., Volume 76 (1979), pp. 333-338

[20] Jungck, G. Compatible mappings and common fixed points , Internat. J. Math. Math. Sci., Volume 9 (1986), pp. 771-779

[21] Jungck, G. Compatible mappings and common fixed points (2), Internat. J. Math. Math. Sci., Volume 9 (1986), pp. 771-779

[22] Jungck, G.; Murthy, P. P.; Cho, Y. J. Compatible mappings of type (A) and common fixed points, Math. Japon, Volume 38 (1993), pp. 381-390

[23] Jungck, G.; Rhoades, B. E. Fixed points for set-valued functions without continuity, Indian J. Pure Appl. Math., Volume 29 (1998), pp. 227-238

[24] Kaneko, H.; S. Sessa Fixed point theorems for compatible multi-valued and single-valued mappings, Internat. J. Math. Math. Sci., Volume 12 (1989), pp. 257-262

[25] Kahn, M. S.; Fisher, B. Some fixed point theorems for commuting mappings, Math. Nachr., Volume 106 (1982), pp. 323-326

[26] Liu, Y.; Wu, J.; Li, Z. Common fixed points of single-valued and multivalued maps, Int. J. Math. Math. Sci., Volume 2005 (2005), pp. 3045-3055

[27] Nadler, S. B. J. Multi-valued contraction mappings, Pacific J. Math., Volume 30 (1969), pp. 475-488

[28] Pathak, H. K.; Agarwal, R. P.; Cho, Y. J. Coincidence and fixed points for multi-valued mappings and its application to nonconvex integral inclusions, J. Comput. Appl. Math., Volume 283 (2015), pp. 201-217

[29] Pathak, H. K.; Cho, Y. J.; Kang, S. M. Remarks on R-weakly commuting mappings and common fixed point theorems, Bull. Korean Math. Soc., Volume 34 (1997), pp. 247-257

[30] Pathak, H. K.; Cho, Y. J.; Kang, S. M.; Lee, B. S. Fixed point theorems for compatible mappings of type (P) and applications to dynamic programming, Le Matematiche, Volume 50 (1995), pp. 15-33

[31] Roldán, A.; Sintunavarat, W. Common fixed point theorems in fuzzy metric spaces using the \((CLR_g)\)-property, Fuzzy Sets and Systems (In press)

[32] Sastry, K. P. R.; Murthy, I. S. R. Krishna Common fixed points of two partially commuting tangential selfmaps on a metric space, J. Math. Anal. Appl., Volume 250 (2000), pp. 731-734

[33] Sessa, S. On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. (Beograd) (N.S.), Volume 32 (1982), pp. 149-153

[34] Sintunavarat, W.; Kumam, P. Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces, J. Appl. Math., Volume 2011 (2011), pp. 1-14

[35] Sintunavarat, W.; Kumam, P. Gregus-type common fixed point theorems for tangential multi-valued mappings of integral type in metric spaces, Internat. J. Math. Math. Sci., Volume 2011 (2011), pp. 1-12

[36] Sintunavarat, W.; Lee, D. M.; Cho, Y. J. Mizoguchi-Takahashi's type common fixed point theorems without T- weakly commuting condition and invariant approximations, Fixed Point Theory Appl., Volume 2014 (2014), pp. 1-10

[37] Wairojjana, N.; Sintunavarat, W.; Kumam, P. Common tripled fixed point theorems for W-compatible mappings along with the \(CLR_g\)-property in abstract metric spaces, J. Inequal. Appl., Volume 2014 (2014), pp. 1-17

Cité par Sources :