Browse > Article
http://dx.doi.org/10.14403/jcms.2012.25.4.617

COMMON FIXED POINTS FOR A COUNTABLE FAMILY OF NON-SELF MULTI-VALUED MAPPINGS ON METRICALLY CONVEX SPACES  

Piao, Yong-Jie (Department of Mathematics Yanbian University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.25, no.4, 2012 , pp. 617-631 More about this Journal
Abstract
In this paper, we will consider some existence theorems of common fixed points for a countable family of non-self multi-valued mappings defined on a closed subset of a complete metrically convex space, and give more generalized common fixed point theorems for a countable family of single-valued mappings. The main results in this paper generalize and improve many common fixed point theorems for single valued or multi-valued mappings with contractive type conditions.
Keywords
common fixed point; metrically convex; complete;
Citations & Related Records
연도 인용수 순위
  • Reference
1 N. A. Assad, Fixed point theorems for set-valued transformations on compact sets, Boll. Un. Math. Ital. 7(4) (1973), 1-7.
2 N. A. Assad, On fixed point theorem of Kannan in Banach spaces, TamKang J. Math. 7 (1976), 91-94.
3 N. A. Assad and W. A. Kirk, Fixed point theorems for set-valued mappings of contractive type, Pacific J. Math. 43 (1972), 553-562.   DOI
4 S. K. Chatterjea, Fixed point theorems, C. R. Acad. Bulagarc Sci. 25 (1972), 727-730.
5 O. Hadzic, Common fixed point theorem for a family of mappings in convex metric spaces, Univ. U. Novom Sadu, Zb. Rad. Prirod. Mat. Fak. Ser. Mat. 20(1) (1990), 89-95.
6 M. S. Khan, H. K. Pathak, and M. D. Khan, Some fixed point theorems in metrically convex spaces, Georgain J. Math. 7(3) (2000), 523-530.
7 I. S. Kim, Common fixed point theorems in 2-metric spaces, Master's Thesis, Korea Soongsil University, Seoul.
8 A. Mujahid, B. E. Rhoades, and N. Talat, Common fixed points of generalized contractive multivalued mappings in cone metric sapces, Math. Commun. 14(2) (2009), 365-378.
9 Y. J. Piao, Unique common fixed point theorems for a family of non-self maps in metrically convex spaces, Math. Appl. 22(4) (2009), 852-857.
10 Y. J. Piao, Unique common fixed points for a family of quasi-contractive type maps in metrically convex spaces, Acta Mathematica Scientia. 30A(2) (2010), 487-493.
11 Y. J. Piao and D. Z. Piao, A family of non-self maps satisfying ${\phi}_i$-contractive condition and having unique common fixed point in metrically convex spaces, Advances in Pure Mathematics. 2(4) (2012), 280-284.   DOI
12 S. L. Singh and B. Ram, Common fixed points of commuting mappings in 2- metric spaces, Math. Sem. Notes 10 (1982), 197-207.
13 J. R. Wu and H. Y. Liu, Common fixed point theorems for sequences of $\Phi$-type contraction set-valued mappings, Chin. Quart. J. Math. 24(4) (2009), 504-510.
14 X. Zhang, Common fixed point theorem of Lipschitz type mappings on cone metric spaces, Acta. Math. Sinica(Chinese Series). 53(6) (2010), 1139-1148.