In this article the invariant centroidal mean is introduced. A pair of double sequences in term Centroidal and its are defined discussed properties monotonicity log-convexity log-concavity. Finally as an illustration it justified that new Gaussian compound CT' ⊗ CT converging faster than H A. 2000 Mathematics Subject Classification. Primary 26D15.

It is known, that under some natural conditions, the iterates of any continuous mean-type mapping converge to a continuous invariant mean-type mapping, and, moreover, the invariant continuous mean-type mapping is unique. In this paper we show that the assumption of the continuity in the ”moreover” part of this result is superfluous. We also show that every increasing and homogeneous mean is con...

In this paper we prove that Bourgain algebra of qX relative to L? contains C if X is backward shift invariant analytic subalgebra and q ? an inner function, i.e. (qX, L?)b C. We also studied some algebras finitely generated ideals in A H?.

We revisit the sequential rate-distortion (SRD) trade-off problem for vector-valued Gauss-Markov sources with mean-squared error distortion constraints. We show via a counterexample that the dynamic reverse water-filling algorithm suggested by [1, eq. (15)] is not applicable to this problem, and consequently the closed form expression of the asymptotic SRD function derived in [1, eq. (17)] is n...