A mean ergodic theorem via weak statistical convergence

In this article, firstly we introduce weak statistical compactness and then, we prove a mean ergodic theorem by using this new concept. Since weak convergence implies weak statistical convergence, our result is a more generalization of Cohen,[3].Publisher's Versio

Weak and weak*I^K-convergence in normed spaces

The main object of this paper is to study the concept of weak $I^K$-convergence, a generalization of weak $I^*$-convergence of sequences in a normed space, introducing the idea of weak* $I^K$-convergence of sequences of functionals where $I,K$ are two ideals on $\mathbb{N}$, the set of all positive integers. Also we have studied the ideas of weak $I^K$ and weak* $I^K$-limit points to investigate the properties in the same space

On lacunary statistical boundedness

A new concept of lacunary statistical boundedness is introduced. It is shown that, for a given lacunary sequence θ={kr}, a sequence {xk} is lacunary statistical bounded if and only if for ‘almost all k w.r.t. θ’, the values xk coincide with those of a bounded sequence. Apart from studying various algebraic properties and computing the Köthe-Toeplitz duals of the space Sθ(b) of all lacunary statistical bounded sequences, a decomposition theorem is also established. We characterize those θ for which Sθ(b)=S(b). Finally, we give a general description of inclusion between two arbitrary lacunary methods of statistical boundedness

Density by Moduli and Statistical Boundedness

We have generalized the notion of statistical boundedness by introducing the concept of f-statistical boundedness for scalar sequences where f is an unbounded modulus. It is shown that bounded sequences are precisely those sequences which are f-statistically bounded for every unbounded modulus f. A decomposition theorem for f-statistical convergence for vector valued sequences and a structure theorem for f-statistical boundedness have also been established

A Class of Sequences Defined by Weak Ideal Convergence and Musielak-Orlicz Function

We introduced the weak ideal convergence of new sequence spaces combining an infinite matrix of complex numbers and Musielak-Orlicz function over normed spaces. We also study some topological properties and inclusion relation between these spaces

A Class of Sequences Defined by Weak Ideal Convergence and Musielak-Orlicz Function

We introduced the weak ideal convergence of new sequence spaces combining an infinite matrix of complex numbers and MusielakOrlicz function over normed spaces. We also study some topological properties and inclusion relation between these spaces

On weak statistical convergence

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