The Krasnosel’skiı̆–Mann (KM) iteration is a widely used method to solve fixed point problems. This paper investigates the convergence rate for the KM iteration. We first establish a new convergence rate for the KM iteration which improves the known big-O rate to little-o without any other restrictions. The proof relies on the connection between the KM iteration and a useful technique on the con...

This paper presents an equational axiomatization of bisimulation equivalence over the language of Basic Process Algebra (BPA) with multi-exit iteration. Multiexit iteration is a generalization of the standard binary Kleene star operation that allows for the specification of agents that, up to bisimulation equivalence, are solutions of systems of recursion equations of the form X1 def = P1X2 +Q1...

In this paper, we consider efficient methods for maximizing x >Bx x>Wx + x>Dx over the unit sphere, where B,D are symmetric matrices, and W is symmetric and positive definite. This problem can arise in the downlink of a multi-user MIMO system and in the sparse Fisher discriminant analysis in pattern recognition. It is already known that the problem of finding a global maximizer is closely assoc...

Convergence proofs for the multi-grid iteration are known for the case of finite element equations and for the case of some difference schemes discretizing boundary value problems in a rectangular region. In the present paper we give criteria of convergence that apply to general difference schemes for boundary value problems in Lipschitzian regions. Furthermore, convergence is proved for the mu...

Dynamical Systems theory generally deals with fixed point iterations of continuous functions. Computation by Turing machine although is a fixed point iteration but is not continuous. This specific category of fixed point iterations can only be studied using their orbits. Therefore the standard notion of chaos is not immediately applicable. However, when a suitable definition is used, it is foun...

Let X be a Banach space and K a nonempty subset of X. The set K is called proximinal if for each x ∈ X, there exists an element y ∈ K such that ‖x − y‖ d x,K , where d x,K inf{‖x − z‖ : z ∈ K}. Let CB K , C K , P K , F T denote the family of nonempty closed bounded subsets, nonempty compact subsets, nonempty proximinal bounded subsets of K, and the set of fixed points, respectively. A multivalu...

In this paper, we consider the convergence of three-step fixed point iterative processes for multivalued nonexpansive mapping with errors, under some different conditions, the sequences of three-step fixed point iterates strongly or weakly converge to a fixed point of the multivalued nonexpansive mapping. Our results extend and improve some recent results.

In this paper, we consider the convergence of three-step fixed point iterative processes for multivalued nonexpansive mapping, under some different conditions, the sequences of three-step fixed point iterates strongly or weakly converge to a fixed point of the multivalued nonexpansive mapping. Our results extend and improve some recent results. Mathematics Subject Classification: 47H09, 47H10, ...

-In this paper, we propose iterative soft-input soft-output (SISO) multi-carrier detection (inter-carrier interference cancellation) and LDPC decoding of the OFDM system in the mobile channel. The proposed SISO multi-carrier detection and sum-product decoding of the LDPC-coded OFDM system can achieve better error rate performance than previous SISO multi-carrier detection and BCJR decoding of c...