This paper concerns with convergence properties of the classical proximal point algorithm for finding zeroes of maximal monotone operators in an infinite-dimensional Hilbert space. It is well known that the proximal point algorithm converges weakly to a solution under very mild assumptions. However, it was shown by Güler [11] that the iterates may fail to converge strongly in the infinite-dimen...

This paper concerns with convergence properties of the classical proximal point algorithm for nding zeroes of maximal monotone operators in an innnite-dimensional Hilbert space. It is well known that the proximal point algorithm converges weakly to a solution under very mild assumptions. However, it was shown by G uler 11] that the iterates may fail to converge strongly in the innnite-dimension...

Many algorithms for approximate reinforcement learning are not known to converge. In fact, there are counterexamples showing that the adjustable weights in some algorithms may oscillate within a region rather than converging to a point. This paper shows that, for two popular algorithms, such oscillation is the worst that can happen: the weights cannot diverge, but instead must converge to a bou...

It is possible (as in [4] ) to define a duality operation f —• f * in the ring of virtual characters of an arbitrary finite group with a split (B, 7V)-pair of characteristic p. Such a group arises as the fixed points under a Frobenius map of a connected reductive algebraic group, defined over a finite field [1]. This paper contains statements of several general properties of the duality map f —...

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, ...

For a sequence of independent observations Zn = (Xn, Yn) from the bivariate standard normal density there are at least three asymptotic descriptions of the sample clouds: • Let rn = √ 2 log n. The sample clouds {Z1/rn, . . . ,Zn/rn} converge onto the closed unit disk E. The probability of a sample point outside a disk of radius r > 1 tends to zero, as does the probability for any m ≥ 1 of less ...

In this paper we construct elliptic boundary value problems whose standard finite element approximations converge arbitrarily slowly in the energy norm, and show that adaptive procedures cannot improve this slow convergence. We also show that the L2-norm and the nodal point errors converge arbitrarily slowly. With the L2-norm two cases need to be distinguished, and the usual duality principle d...