Let c be the Banach space consisting of all convergent sequences of reals with the sup-norm, $C_{\infty }(A,c)$ the set of all bounded continuous functions f: A → c, and $C_A(X,c)$ the set of all functions f: X → c which are continuous at each point of A ⊂ X. We show that a Tikhonov subspace A of a topological space X is strong Choquet in X if there exists a monotone extender $u:C_{\infty }(A,c)\to C_A(X,c)$. This shows that the monotone extension property for bounded c-valued functions can fail in GO-spaces, which provides a negative answer to a question...

The paper deals with the properties of a monotone operator defined on a subset of an ordered Banach space. The structure of the set of fixed points between the minimal and maximal ones is described.

We characterize Banach lattices under which each b-weakly compact (resp. b-AM-compact, strong type (B)) operator is L-weakly compact (resp. M-weakly compact).