in this paper, the notion of n, pn - summability to generalize the concept of statisticalconvergence is used. we call this new method weighted statistically convergence. we also establish itsrelationship with statistical convergence, c,1-summability and strong   n n, p -summability.

We study convergence of positive solutions for almost periodic reaction diffusion equations of Fisher or Kolmogorov type. It is proved that under suitable conditions every positive solution is asymptotically almost periodic. Moreover, all positive almost periodic solutions are harmonic and uniformly stable, and if one of them is spatially homogeneous, then so are others. The existence of an alm...

lorentz characterized the almost convergence through the concept of uniform convergence of de lavallée-poussin mean. in this paper, we generalize the notion of almost convergence by using the concept ofinvariant mean and the generalized de la vallée-poussin mean. we determine the bounded linear operators forthe generalized σ-conservative, σ-regular and σ-coercive matrices.

The purpose of this paper is to introduce the concept of4m vλ strongly almost convergence with respect to a sequence of moduli and4m vλ Almost Statistical Convergence and give some relations between these two kinds of convergence. 2000 Mathematics Subject Classification: 40A05,40C05, 46A45.

In this paper, we first give the concept of properly distributed sequence, and prove that it is almost convergent with F-limit expressed as a formal integral. Basing on these, we review the work of Feng and Li, which is shown to be a special case of our generalized theory. Then we generalize Banach limit to Banach limit functional, which is the minimum requirement to characterize strong almost ...