Fixed points and best approximation in Menger convex metric spaces
Beg, Ismat ; Abbas, Mujahid
Archivum Mathematicum, Tome 041 (2005), p. 389-397 / Harvested from Czech Digital Mathematics Library

We obtain necessary conditions for the existence of fixed point and approximate fixed point of nonexpansive and quasi nonexpansive maps defined on a compact convex subset of a uniformly convex complete metric space. We obtain results on best approximation as a fixed point in a strictly convex metric space.

Publié le : 2005-01-01
Classification:  47H09,  47H10,  54H25
@article{107968,
     author = {Ismat Beg and Mujahid Abbas},
     title = {Fixed points and best approximation in Menger convex metric spaces},
     journal = {Archivum Mathematicum},
     volume = {041},
     year = {2005},
     pages = {389-397},
     zbl = {1109.47047},
     mrnumber = {2195492},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107968}
}
Beg, Ismat; Abbas, Mujahid. Fixed points and best approximation in Menger convex metric spaces. Archivum Mathematicum, Tome 041 (2005) pp. 389-397. http://gdmltest.u-ga.fr/item/107968/

Aksoy A. G.; Khamsi M. A. Nonstandard methods in fixed point theory, Springer, New York, Berlin, 1990. (1990) | MR 1066202 | Zbl 0713.47050

Aronszajn N.; Panitchpakdi P. Extension of uniformly continuous transformations and hyper convex metric spaces, Pacific J. Math. 6 (1956), 405–439. (1956) | MR 0084762

Ayerbe Toledano J. M.; Dominguez Benavides T.; Lopez Acedo G. Measures of noncompactness in metric fixed point theory, Birkhauser, Basel, 1997. (1997) | MR 1483889 | Zbl 0885.47021

Beg I.; Azam A. Fixed points of asymptotically regular multivalued mappings, J. Austral. Math. Soc. Ser. A 53(3) (1992), 313–326. (1992) | MR 1187851 | Zbl 0765.54036

Beg I.; Azam A. Common fixed points for commuting and compatible maps, Discuss. Math. Differential Incl. 16 (1996), 121–135. (1996) | MR 1646650 | Zbl 0912.47033

Berard A. Characterization of metric spaces by the use of their mid sets intervals, Fund. Math. 73 (1971), 1–7. (1971) | MR 0295300

Blumenthal L. M. Distance Geometry, Clarendon Press, Oxford, 1953. (1953) | MR 0054981 | Zbl 0050.38502

Browder F. E. Nonexpansive nonlinear operators in Banach spaces, Proc. Nat. Acad. Sci. U.S.A. 54 (1965), 1041–1044. (1965) | MR 0187120

Dotson W. G. On fixed points of nonexpansive mappings in non convex sets, Proc. Amer. Math. Soc. 38 (1973), 155–156. (1973) | MR 0313894

Goeble K.; Kirk W. A. Topics in metric fixed point theory, Cambridge Stud. Adv. Math. 28, Cambridge University Press, London, 1990. (1990) | MR 1074005

Goeble K.; Reich S. Uniform convexity, hyperolic geometry, and nonexpansive mappings, Marcel Dekker, Inc. New York and Basel (1984). (1984) | MR 0744194

Gohde D. Zum Prinzip der kontraktiven Abbildung, Math. Nachr. 30 (1995), 251–258. (1995) | MR 0190718

Habiniak L. Fixed point theorem and invarient approximation, J. Approx. Theory 56 (1984), 241–244. (1984)

Hadzic O. Almost fixed point and best approximation theorems in H-Spaces, Bull. Austral. Math. Soc. 53 (1996), 447–454. (1996) | MR 1388593

Khalil R. Extreme points of the unit ball of Banach spaces, Math. Rep. Toyama Univ. 4 (1981), 41–45. (1981) | MR 0627961 | Zbl 0473.46012

Khalil R. Best approximation in metric spaces, Proc. Amer. Math. Soc. 103 (1988), 579–586. (1988) | MR 0943087 | Zbl 0652.51019

Kirk W. A. A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly 72 (1965), 1004–1006. (1965) | MR 0189009 | Zbl 0141.32402

Menger K. Untersuchungen über allegemeine Metrik, Math. Ann. 100 (1928), 75–63. (1928) | MR 1512479

Prus B.; Smarzewski R. S. Strongly unique best approximation and centers in uniformly convex spaces, J. Math. Anal. Appl. 121 (1978), 85–92. (1978) | MR 0869515

Veeramani P. On some fixed point theorems on uniformly convex Banach spaces, J. Math. Anal. Appl. 167 (1992), 160–166. (1992) | MR 1165265 | Zbl 0780.47047