The main object of this paper is to introduce a new concept of weak statistically Cauchy sequence in a normed space. It is shown that in a reflexive space, weak statistically Cauchy sequences are the same as weakly statistically convergent sequences. Finally, weak statistical convergence has been discussed in l p spaces. under the Creative Commons Attribution License, which permits unrestricted...

In this paper a proximal point algorithm (PPA) for maximal monotone operators with appropriate regularization parameters is considered. A strong convergence result for PPA is stated and proved under the general condition that the error sequence tends to zero in norm. Note that R.T. Rockafellar (1976) assumed summability for the error sequence to derive weak convergence of PPA in its initial for...

Abstract Topological measures and deficient topological are defined on open closed subsets of a space, generalize regular Borel measures, correspond to (nonlinear in general) functionals that linear singly generated subalgebras or cones functions. They lack subadditivity, many standard techniques measure theory functional analysis do not apply them. Nevertheless, we show classical results proba...

The additive model is one of the most popular semiparametric models. The backfitting estimation (Buja, Hastie and Tibshirani, 1989, Ann. Statist.) for the model is intuitively easy to understand and theoretically most efficient (Opsomer and Ruppert, 1997, Ann. Statist.); its implementation is equivalent to solving simple linear equations. However, convergence of the algorithm is very difficult ...

The main purpose of this paper is to establish different types of convergence theorems for fuzzy Henstock integrable functions, introduced by  Wu and Gong cite{wu:hiff}. In fact, we have proved fuzzy uniform convergence theorem, convergence theorem for fuzzy uniform Henstock integrable functions and fuzzy monotone convergence theorem. Finally, a necessary and sufficient condition under which th...