Let be a partial order on a countable set V such that there exists a minimum element a ∈ V and {u ∈ V : u v} is finite for each v ∈ V . An item of information is to be broadcast to the elements of V according to the policy in the following sense: a is initially informed and broadcasting to v 6= a begins as soon as all elements u ≺ v are informed; the time required to broadcast the information i...

In this paper, we introduce a concept of a generalized $c$-distance in ordered cone $b$-metric spaces and, by using the concept, we prove some fixed point theorems in ordered cone $b$-metric spaces. Our results generalize the corresponding results obtained by Y. J. Cho, R. Saadati, Shenghua Wang (Y. J. Cho, R. Saadati, Shenghua Wang, Common fixed point  heorems on generalized distance in ordere...

The (in)equational properties of the least fixed point operation on ( -)continuous functions on ( -)complete partially ordered sets are captured by the axioms of (ordered) iteration algebras, or iteration theories. We show that the inequational laws of the sum operation in conjunction with the least fixed point operation in continuous additive algebras have a finite axiomatization over the ineq...