In this work we introduce and investigate the ideas of statistical Riemann integrability, summability, Lebesgue integrability summability via deferred weighted mean. We first establish some fundamental limit theorems connecting these beautiful potentially useful notions. Furthermore, based upon our proposed techniques, Korovkin-type approximation with algebraic test functions. Finally, present ...

Summability is an important concept in sequence spaces. One summability strongly Cesaro summable. In this paper, we study a subset of the set all vector-valued 2-modular space. Some facts that investigated paper include linearity, existence modular and completeness with respect to these modular.

In this article, we investigate the summability of formal power series solutions in time inhomogeneous heat equation with a power-law nonlinearity degree two, and variable coefficients. particular, give necessary sufficient conditions for 1-summability given direction. These generalize ones linear by W. Balser M. Loday-Richaud 2009 article [5].

In this paper, using the fractional difference operator and a modulus function we introduce concepts of $({}^{}_{2}{\Delta_{\beta}^{\tilde{\alpha}}},f)-$ statistical convergence, $({}^{}_{2}{\Delta^{\tilde{\alpha}}},f)-$ Cauchy p-strongly Cesàro summability, $(0<p<\infty)$ for double sequences. We also give some inclusion relations between convergence summability $(0<p<\infty)$.

In this paper we establish a Tauberian condition under which convergence follows from H"{o}lder summability of sequences of fuzzy  numbers.

In this paper, we present statistical weighted mean ( briefly, (N?,p,q,1,1)) summability method for double sequences of fuzzy numbers and give necessary sufficient Tauberian conditions under which convergence a sequence follows from its (N?,p,q,1,1) summability. Furthermore, apply our new to prove Korovkin type approximation theorem positive linear operators.

We investigate Gevrey order and 1-summability properties of the formal solution of a general heat equation in two variables. In particular, we give necessary and sufficient conditions for the 1-summability of the solution in a given direction. When restricted to the case of constants coefficients, these conditions coincide with those given by D. A. Lutz, M. Miyake, R. Schäfke in a 1999 article ...

In this paper we study the one-sided shift operator on a state space defined by a finite alphabet. Using a scheme developed by Walters [13], we prove that the sequence of iterates of the transfer operator converges under square summability of variations of the g-function, a condition which gave uniqueness of a g-measure in [7]. We also prove uniqueness of so-called G-measures, introduced by Bro...

Xinmin Wu ([email protected]) Helle Oerding ([email protected]) Jin Liu ([email protected]) Bernard Vanacker ([email protected]) Shanglong Yao ([email protected]) Vegard Dahl ([email protected]) Lize Xiong ([email protected]) Casper Claudius ([email protected]) Yun Yue ([email protected]) Yuguang Huang ([email protected]) Esther Abels ([email protected]) Henk Rietberge...

Given the Sturm-Liouville eigenfunction expansion of an ¿2 function fix), summability theory provides means for recovering the value of fix¿) at points x0 where / is sufficiently regular. If the coefficients in the expansion are perturbed slightly (in the I^ norm), a stable summation method will recover from the perturbed expansion a good approximation to fix¿). In this paper we develop stable ...