in this work, a new iterative method is proposed for obtaining the approximate solution of a class of hammerstein type integral equations system. the main structure of this method is based on the richardson iterative method for solving an algebraic linear system of equations. some conditions for existence and unique solution of this type equations are imposed. convergence analysis and error bou...

In this paper we present new iterative algorithms in convex metric spaces. We show that these iterative schemes are convergent to the fixed point of a single-valued contraction operator. Then we make the comparison of their rate of convergence. Additionally, numerical examples for these iteration processes are given.

This note studies Arveson’s curvature invariant for d-contractions T = (T1, T2, . . . , Td) for the special case d = 1, referring to a single contraction operator T on a Hilbert space. It establishes a formula which gives an easy-to-understand meaning for the curvature of a single contraction. The formula is applied to give an example of an operator with nonintegral curvature. Under the additio...

It is shown that if a paranormal contraction T has no nontrivial invariant subspace, then it is a proper contraction. Moreover, the nonnegative operator Q = T 2∗T 2 − 2T ∗T + I also is a proper contraction. If a quasihyponormal contraction has no nontrivial invariant subspace then, in addition, its defect operator D is a proper contraction and its itself-commutator is a trace-class strict contr...

This paper presents a framework for relevance-based belief change in propositional Horn logic. We firstly establish a parallel interpolation theorem for Horn logic and show that Parikh’s Finest Splitting Theorem holds with Horn formulae. By reformulating Parikh’s relevance criterion in the setting of Horn belief change, we construct a relevance-based partial meet Horn contraction operator and p...

Recently, Sutton et al. (2015) introduced the emphatic temporal differences (ETD) algorithm for off-policy evaluation in Markov decision processes. In this short note, we show that the projected fixed-point equation that underlies ETD involves a contraction operator, with a √ γ-contraction modulus (where γ is the discount factor). This allows us to provide error bounds on the approximation erro...

In this paper we show that every power bounded operator weighted shift with commuting normal weights is similar to a contraction. As an application of this result, we reduce the problem whether every centered power bounded operator is similar to a contraction to the analogous question about quasi-invertible centered operators.

Let (H,B) be an abstract Wiener space and let μs be the Gaussian measure on B with variance s. Let ∆ be the Laplacian (not the number operator), that is, a sum of squares of derivatives associated to an orthonormal basis of H. I will show that the heat operator exp(t∆/2) is a contraction operator from L2(B,μs) to L2(B,μs−t), for all t < s. More generally, the heat operator is a contraction from...