Introduction This paper tries to shed some light on the very classical topic of overconvergence for Dirichlet series, by employing results in the theory of innite order dier-ential operators with constant coecients ([3], [13]). The possibility of linking innite order dierential operators with gap theorems and related subjects such as overconvergence phenomena was rst suggested by Ehrenpreis in ...

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...

and Applied Analysis 3 the fixed point theory and that a Banach space X has property L if and only if it is reflexive and has the uniform Opial property. For a real vector space X, a function ρ : X → 0,∞ is called amodular if it satisfies the following conditions: i ρ x 0 if and only if x 0; ii ρ αx ρ x for all scalar α with |α| 1; iii ρ αx βy ≤ ρ x ρ y , for all x, y ∈ X and all α, β ≥ 0 with ...

Abstract In this study, by using definition of ρ -statistical convergence which was defined Çakallı [5], we introduce the concepts pointwise w α ( f )-summability, order and uniform sequences real-valued functions. Also, give some inclusion relations between these concepts.