Ideal convergence of continuous functions

Statistical Convergence and Ideal Convergence for Sequences of Functions

Let I ⊂ P(N) stand for an ideal containing finite sets. We discuss various kinds of statistical convergence and I-convergence for sequences of functions with values in R or in a metric space. For real valued measurable functions defined on a measure space (X,M, μ), we obtain a statistical version of the Egorov theorem (when μ(X) < ∞). We show that, in its assertion, equi-statistical convergence...

Purity of the Ideal of Continuous Functions with Pseudocompact Support

Let CΨ (X) be the ideal of functions with pseudocompact support and let kX be the set of all points in υX having compact neighborhoods. We show that CΨ (X) is pure if and only if βX−kX is a round subset of βX, CΨ (X) is a projective C(X)-module if and only if CΨ (X) is pure and kX is paracompact. We also show that if CΨ (X) is pure, then for each f ∈ CΨ (X) the ideal (f ) is a projective (flat)...

Statistical Convergence and Ideal Convergence of Sequences of Functions in 2-Normed Spaces

On The Mean Convergence of Biharmonic Functions

Let denote the unit circle in the complex plane. Given a function , one uses t usual (harmonic) Poisson kernel for the unit disk to define the Poisson integral of , namely . Here we consider the biharmonic Poisson kernel for the unit disk to define the notion of -integral of a given function ; this associated biharmonic function will be denoted by . We then consider the dilations ...

Rough Ideal Convergence

In this paper we extend the notion of rough convergence using the concept of ideals which automatically extends the earlier notions of rough convergence and rough statistical convergence. We define the set of rough ideal limit points and prove several results associated with this set.