In this paper we define the sequence space ∆v (X) = {x ∈ w : (∆v xk) ∈ X}, (m ∈ N) , where ∆v xk = ∑m i=0 (−1) ( m i ) xk+ivk+i and X is any sequence space. We give some relations related to this space. Furthermore we introduce the concept of ∆v −statistical convergence and give some inclusion relation between ∆v (wp)−convergence and ∆v −statistical convergence.

We present in this paper several asymptotic properties of constrained Markov Decision Processes (MDPs) with a countable state space. We treat both the discounted and the expected average cost, with unbounded cost. We are interested in (1) the convergence of nite horizon MDPs to the innnite horizon MDP, (2) convergence of MDPs with a truncated state space to the problem with innnite state space,...

In this paper, we study the complete convergence and complete moment convergence for weighted sums of extended negatively dependent (END) random variables under sub-linear expectations space with the condition of [Formula: see text], further [Formula: see text], [Formula: see text] ([Formula: see text] is a slow varying and monotone nondecreasing function). As an application, the Baum-Katz type...

The aim of this paper is to set up appropriate uniform convergence spaces in which to reformulate and enrich the Order Completion Method [25] for nonlinear PDEs. In this regard, we consider an appropriate space ML (X) of normal lower semi-continuous functions. The space ML (X) appears in the ring theory of C (X) and its various extensions [15], as well as in the theory of nonlinear, PDEs [25] a...

In this paper we introduce a broad class of nonlinear mappings which contains the class of contractive mappings and the class of generalized hybrid mappings in a Hilbert space. Then we prove an attractive point theorem for such mappings in a Hilbert space. Furthermore, we prove a mean convergence theorem of Baillon’s type without convexity in a Hilbert space. Finally, we prove a weak convergenc...