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.

In this paper we present some results on convergence and summability of oneand multi-dimensional trigonometric andWalsh-Fourier series. The Fejér and Cesàro summability methods are investigated. We will prove that the maximal operator of the summability means is bounded from the corresponding classical or martingale Hardy space Hp to Lp for some p > p0. For p = 1 we obtain a weak type inequalit...

We have established a relation between θ−|R,pn|k and θ−|R,qn|k summability methods, k > 1, which generalizes a result of Sunouchi (1949) on |R,pn| and |R,qn| summability methods.

In [1] we uniquely introduced ultra exponential functions (uxpa) and denednext step of the serial binary operations: addition, multiplication and power.Also, we exhibited the topic of limit summability of real functions in [2,3]. Inthis paper, we study limit summability of the ultra exponential functions andprove some of their properties. Finally, we pose an unsolved problem aboutthem.

In this paper‎, ‎following a very recent‎ ‎and new approach‎, ‎we further generalize recently introduced‎ ‎summability methods‎, ‎namely‎, ‎$I$-statistical convergence and‎ ‎$I$-lacunary statistical convergence (which extend the important‎ ‎summability methods‎, ‎statistical convergence and lacunary‎ ‎statistical convergence using ideals of $mathbb{N}$) and‎ ‎introduce the notions of $I$-statis...

In this paper we use the idea of logarithmic density to define the concept of logarithmic statistical convergence. We find the relations of logarithmic statistical convergence with statistical convergence, statistical summability (H, 1) introduced by Móricz (Analysis 24:127-145, 2004) and [H, 1]q-summability. We also give subsequence characterization of statistical summability (H, 1). MSC: 40A0...

In this paper, a one-sided condition is given to recover .C; ̨/ summability of a sequence from its .A/.C; ̨C 1/ summability. Our result extends and generalizes the well known classical Tauberian theorems given for Abel and Cesàro summability methods. 2010 Mathematics Subject Classification: 40E05; 40G05; 40G10

We consider the linear elliptic equation −div(a∇u) = f on some bounded domain D, where a has the form a = exp(b) with b a random function defined as b(y) = ∑ j≥1 yjψj where y = (yj) ∈ RN are i.i.d. standard scalar Gaussian variables and (ψj)j≥1 is a given sequence of functions in L∞(D). We study the summability properties of Hermite-type expansions of the solution map y 7→ u(y) ∈ V := H 0 (D), ...

We extended a theorem of Mishra and Srivastava (1983–1984) on |C,1|k summability factors, using almost increasing sequences, to |N̄,pn|k summability under weaker conditions.

Some recent results on a general summability method, on the so-called θ-summability is summarized. New spaces, such as Wiener amalgams, Feichtinger’s algebra and modulation spaces are investigated in summability theory. Sufficient and necessary conditions are given for the norm and a.e. convergence of the θ-means.