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Zbl 1230.47083
Kuaket, Kitima; Kumam, Poom
Fixed points of asymptotic pointwise contractions in modular spaces.
(English)
[J] Appl. Math. Lett. 24, No. 11, 1795-1798 (2011). ISSN 0893-9659

Summary: {\it W. A. Kirk} and {\it H.-K. Xu} [Nonlinear Anal., Theory Methods Appl. 69, No.~12, A, 4706--4712 (2008; Zbl 1172.47038)] introduced the concept of asymptotic pointwise contractions. In this paper, we investigate these kinds of mappings in modular spaces. Moreover, the fixed point theorem for asymptotic pointwise nonexpansive mappings in modular spaces is also studied. The results of this paper improve and extend the results of {\it A. Razani}, {\it E. Nabizadeh}, {\it M. B. Mohamadi} and {\it S. H. Pour} [Abstr. Appl. Anal. 2007, Article ID 40575 (2007; Zbl 1152.47043)], and {\it W. A. Kirk} and {\it H.-K. Xu} [loc.\,cit.] to modular spaces.
MSC 2000:
*47H09 Mappings defined by "shrinking" properties
46A80 Modular spaces
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: asymptotic pointwise contractions; asymptotic pointwise nonexpansive; modular spaces; fixed points; convex modular

Citations: Zbl 1172.47038; Zbl 1152.47043

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