It is well known from the classical theory of trigonometric series that the series (1) cannot converge except possibly for values of x in a set of zero Lebesgue measure . Our object is to discover how `thin' this set is for various types of sequence {nk } . The first result of this kind is due to P . Turan who proved, in 1941, that the series (1) converges absolutely in a set of positive logari...

3.5 Consistency of approximate M-estimators of ψ type. As in Sec. 3.3, let (X, A, P) be a probability space and Θ a locally compact separable metric space. Let ψ(θ, x) be a function of x in X and θ ∈ Θ with values in a Euclidean space R m. Let X 1 , X 2 ,. .. be independent with values in X and distribution P. A sequence of estimators T n := T n (X 1 ,. .. , X n) with values in Θ will be called...

In the following the symbol 0 is used to denote the composition of functions. A superscript of the form (p) where p is a nonnegative integer will indicate the p-th derivative of a function. For example, if Hand g are differentiable functions, then Hog(I)(t) = ftH(g(t)). Wherever used, K1, K2, ... will represent appropriate constants. E and P will be used for expectation and probability, respect...

In this paper we study front tracking for a model of one dimensional, immiscible flow of several isentropic gases, each governed by a gammalaw. The model consists of the p-system with variable gamma representing the different gases. The main result is the convergence of a front tracking algorithm to a weak solution, thereby giving existence as well. This convergence holds for general initial da...

In this paper we introduce strongly $left[  V_{2},lambda_{2},M,pright]-$summable double vsequence spaces via Orlicz function and examine someproperties of the resulting these spaces. Also we give natural relationshipbetween these spaces and $S_{lambda_{2}}-$statistical convergence.