Fixed point theorems for nonexpansive mappings in modular spaces
Kumam, Poom
Archivum Mathematicum, Tome 040 (2004), p. 345-353 / Harvested from Czech Digital Mathematics Library
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In this paper, we extend several concepts from geometry of Banach spaces to modular spaces. With a careful generalization, we can cover all corresponding results in the former setting. Main result we prove says that if $\rho $ is a convex, $\rho $-complete modular space satisfying the Fatou property and $\rho _r$-uniformly convex for all $r>0$, C a convex, $\rho $-closed, $\rho $-bounded subset of $X_\rho $, $T:C\rightarrow C$ a $\rho $-nonexpansive mapping, then $T$ has a fixed point.

Publié le : 2004-01-01
Classification:  46A80,  46B20,  46E30,  47H09,  47H10 
@article{107918,
     author = {Poom Kumam},
     title = {Fixed point theorems for nonexpansive mappings in modular spaces},
     journal = {Archivum Mathematicum},
     volume = {040},
     year = {2004},
     pages = {345-353},
     zbl = {1117.47045},
     mrnumber = {2129956},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107918}
}

Kumam, Poom. Fixed point theorems for nonexpansive mappings in modular spaces. Archivum Mathematicum, Tome 040 (2004) pp. 345-353. http://gdmltest.u-ga.fr/item/107918/

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