we then write sn → s(A), where A is the A method of summability. Appropriate choices of A= [an,k] for n,k ≥ 0 give the classical methods [2]. In this paper, we present various summability analogs of the strong law of large numbers (SLLN) and their rates of convergence in an unified setting, beyond the class of random-walk methods. A convolution summability method introduced in the next section ...

In this paper we have proved some theorems on weighted mean summability method by using analytical and summability techniques, which also extends the well known result of Hardy on the Cesàro 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 study we introduce the concepts of statistical convergence of order$beta$ and strong $p-$Ces`{a}ro summability of order $beta$ for sequencesof fuzzy numbers. Also, we give some relations between the statisticalconvergence of order $beta$ and strong $p-$Ces`{a}ro summability of order$beta$ and construct some interesting examples.

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 prove that a stationary max–infinitely divisible process is mixing (ergodic) iff its dependence function converges to 0 (is Cesaro summable to 0). These criteria are applied to some classes of max–infinitely divisible processes.