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Search: MSC category 47H09 ( Contraction-type mappings, nonexpansive mappings, \$A\$-proper mappings, etc. )

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1. CMB Online first

Alfuraidan, Monther Rashed
 The Contraction Principle for Multivalued Mappings on a Modular Metric Space with a Graph We study the existence of fixed points for contraction multivalued mappings in modular metric spaces endowed with a graph. The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, were recently introduced. This paper can be seen as a generalization of Nadler's and Edelstein's fixed point theorems to modular metric spaces endowed with a graph. Keywords:fixed point theory, modular metric spaces, multivalued contraction mapping, connected digraph.Categories:47H09, 46B20, 47H10, 47E10

2. CMB Online first

Khamsi, M. A.
 Approximate Fixed Point Sequences of Nonlinear Semigroup in Metric Spaces In this paper, we investigate the common approximate fixed point sequences of nonexpansive semigroups of nonlinear mappings \$\{T_t\}_{t \geq 0}\$, i.e., a family such that \$T_0(x)=x\$, \$T_{s+t}=T_s(T_t(x))\$, where the domain is a metric space \$(M,d)\$. In particular we prove that under suitable conditions, the common approximate fixed point sequences set is the same as the common approximate fixed point sequences set of two mappings from the family. Then we use the Ishikawa iteration to construct a common approximate fixed point sequence of nonexpansive semigroups of nonlinear mappings. Keywords:approximate fixed point, fixed point, hyperbolic metric space, Ishikawa iterations, nonexpansive mapping, semigroup of mappings, uniformly convex hyperbolic spaceCategories:47H09, 46B20, 47H10, 47E10

3. CMB 1998 (vol 41 pp. 413)

Llorens-Fuster, Enrique; Sims, Brailey
 The fixed point property in \$\lowercase{c_0}\$ A closed convex subset of \$c_0\$ has the fixed point property (\$\fpp\$) if every nonexpansive self mapping of it has a fixed point. All nonempty weak compact convex subsets of \$c_0\$ are known to have the \$\fpp\$. We show that closed convex subsets with a nonempty interior and nonempty convex subsets which are compact in a topology slightly coarser than the weak topology may fail to have the \$\fpp\$. Categories:47H09, 47H10