In this paper, we prove the following strong convergence theorem: Let C be a closed convex subset of a Hilbert space H. Let {T (t) : t ≥ 0} be a strongly continuous semigroup of nonexpansive mappings on C such that ⋂ t≥0 F ( T (t) ) 6= ∅. Let {αn} and {tn} be sequences of real numbers satisfying 0 < αn < 1, tn > 0 and limn tn = limn αn/tn = 0. Fix u ∈ C and define a sequence {un} in C by un = (...

This paper is devoted to the convergence rate estimate for the method of successive subspace corrections applied to symmetric and positive semidefinite (singular) problems. In a general Hilbert space setting, a convergence rate identity is obtained for the method of subspace corrections in terms of the subspace solvers. As an illustration, the new abstract theory is used to show uniform converg...

Limiting results for the posterior precision of the states are provided for discount Bayesian state space models. Time varying design vectors are considered as well as the usual constant design vectors. Limiting observability is defined as a useful measure of the suitability of the model. The rate of convergence is explored and conditions of the existence of the limiting posterior precision are...

In this paper, we propose a viscosity iteration process for semigroup of asymptotically pseudocontractive mappings, and prove a strong convergence theorem in uniformly convex Banach space for the proposed iteration process.

In this paper we prove the convergence of algebraically stable DIRK schemes applied to dissipative evolution equations on Hilbert spaces. The convergence analysis is unconditional as we do not impose any restrictions on the initial value or assume any extra regularity of the solution. The analysis is based on the observation that the schemes are linear combinations of the Yosida approximation, ...

We analyse the behaviour of the newly introduced cyclic Douglas–Rachford algorithm for finding a point in the intersection of a finite number of closed convex sets. This work considers the case in which the target intersection set is possibly empty. 1. Preliminaries and Notation Throughout we assume H is a (real) Hilbert space with inner product 〈·, ·〉 and induced norm ‖ · ‖. We use → (resp. w....

Let {Xn, n > 1} be a sequence of coordinatewise negatively associated random vectors taking values in a real separable Hilbert space with the kth partial sum Sk, k > 1. We provide conditions for the convergence of ∑∞ n=1 1 n P(max16k6n ‖Sk‖ > εn α) and ∑∞ n=1 logn n P(max16k6n ‖Sk‖ > εn α) for all ε > 0. The converses of these results are also discussed.

The purpose of this paper is to establish some weak convergence theorems of modified two-step iteration process with errors for two asymptotically quasi-nonexpansive non-self mappings in the setting of real uniformly convex Banach spaces if E satisfies Opial’s condition or the dual E∗ of E has the Kedec-Klee property. Our results extend and improve some known corresponding results from the exis...

We propose a general iterative scheme for solving a generalized equilibrium problem and fixed points of nonexpansive mappings in a Hilbert space. We then prove strong convergence theorems. Mathematics Subject Classification: 47H09, 47H10

In this paper, we continue to study convergence problems for a Ishikawa-like iterative process for a finite family of m-accretive mappings. Strong convergence theorems are established in uniformly smooth Banach spaces.