This paper shows the convergence of the value iteration (or successive approximations) algorithm for average cost (AC) Markov control processes on Borel spaces, with possibly unbounded cost, under appropriate hypotheses on weighted norms for the cost function and the transition law. It is also shown that the aforementioned convergence implies strong forms of AC-optimality and the existence of f...

In this paper, several weak and strong convergence theorems are established for a new modified iterations with errors for finite family of nonself asymptotically nonexpansive mappings in Banach spaces. Mann-type, Ishikawa-type and Noor-type iterations are covered by the new iteration scheme. Our convergence theorems improve, unify and generalize many important results in the current literatures.

In this paper, we define a kind of lattice-valued convergence spaces based on the notion of $top$-filters, namely $top$-convergence spaces, and show the category of $top$-convergence spaces is Cartesian-closed. Further, in the lattice valued context of a complete $MV$-algebra, a close relation between the category of$top$-convergence spaces and that of strong $L$-topological spaces is establish...

In this article we first discuss the existence and uniqueness of a solution for the coincidence problem: Find p ∈ X such that Tp = Sp, where X is a nonempty set, Y is a complete metric space, and T,S :X → Y are two mappings satisfying a Wardowski type condition of contractivity. Later on, we will state the convergence of the Picard-Juncgk iteration process to the above coincidence problem as we...

for solving large sparse non-hermitian positive definite linear equations, bai et al. proposed the hermitian and skew-hermitian splitting methods (hss). they recently generalized this technique to the normal and skew-hermitian splitting methods (nss). in this paper, we present an accelerated normal and skew-hermitian splitting methods (anss) which involve two parameters for the nss iteration. w...

In this paper, we introduce a new Jungck-three step iterative scheme and call it modified three-step iteration process. A strong convergence theorem is proved using this iterative process for the class of generalized contractive-like operators introduced by Olatinwo [14] and Bosede [3] respectively, in a Banach space. The results obtained in this paper improve and generalize among others, the r...