On some basic properties of cones with proofs independent of Zorn’s Lemma

Without the use of Zorn’s Lemma there are the proofs for such two basic properties of cones given in normed spaces that a regular minihedral cone is strongly minihedral and that an increasing self-mapping on order interval induced by regular cone has minimal and maximal fixed points which have been proved in some references by virtue of Zorn’s lemma. We also show that a strongly minihedral generating cone is minihedral. At last, two cones in continuous function space are discussed as examples.

Weak and Strong Limit Theorems for Stochastic Processes under Nonadditive Probability

This paper extends laws of large numbers under upper probability to sequences of stochastic processes generated by linear interpolation. This extension characterizes the relation between sequences of stochastic processes and subsets of continuous function space in the framework of upper probability. Limit results for sequences of functional random variables and some useful inequalities are also obtained as applications.

Fixed Point Theorems and Uniqueness of the Periodic Solution for the Hematopoiesis Models

We present some results to the existence and uniqueness of the periodic solutions for the hematopoiesis models which are described by the functional differential equations with multiple delays. Our methods are based on the equivalent norm techniques and a new fixed point theorem in the continuous function space.

Properties (V) and (w V) on C(Ω X)

A formal series Σxn in a Banach space X is said to be weakly unconditionally converging, or alternatively weakly unconditionally Cauchy (wuc) if Σ|x*(xn)| < ∞ for every continuous linear functional x* ∈ X*. A subset K of X* is called a V-subset of X* iffor each wuc series Σxn in X. Further, the Banach space X is said to have property (V) if the V-subsets of X* coincide with the relatively weakly compact subsets of X*. In a fundamental paper in 1962, Pelczynski [10] showed that the Banach space X has property (V) if and only if every unconditionally converging operator with domain X is weakly compact. In this same paper, Pelczynski also showed that all C(Ω) spaces have property (V), and asked if the abstract continuous function space C(Ω, X) has property (F) whenever X has property (F).