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On locally solid topological lattice groups

Abdul Rahim Khan; Keith Rowlands — 2007

Czechoslovak Mathematical Journal

Let $(G, τ)$ be a commutative Hausdorff locally solid lattice group. In this paper we prove the following: (1) If $(G, τ)$ has the $A$ (iii)-property, then its completion $(\hat{G}, \hat{τ})$ is an order-complete locally solid lattice group. (2) If $G$ is order-complete and $τ$ has the Fatou property, then the order intervals of $G$ are $τ$ -complete. (3) If $(G, τ)$ has the Fatou property, then $G$ is order-dense in $\hat{G}$ and $(\hat{G}, \hat{τ})$ has the Fatou property. (4) The order-bound topology on any commutative lattice group is the finest locally solid topology on...

Characterizations of random approximations

Abdul Rahim Khan; Nawab Hussain — 2003

Archivum Mathematicum

Some characterizations of random approximations are obtained in a locally convex space through duality theory.

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On locally solid topological lattice groups

Characterizations of random approximations

Properties of fixed point set of a multivalued map.

Common fixed points of generalized contractive hybrid pairs in symmetric spaces.

Random fixed points for *-nonexpansive random operators.

On some properties of Banach operators.

A stochastic version of Fan's best approximation theorem.

Approximating fixed points of some maps in uniformly convex metric spaces.

Strong convergence of an implicit algorithm in CAT(0) spaces.

Convergence of implicit iterates with errors for mappings with unbounded domain in Banach spaces.