We prove a general theorem on |N̄,pn;δ|k summability factors, which generalizes a theorem of Bor (1994) on |N̄,pn|k summability factors, under weaker conditions by using an almost increasing sequence. 2000 Mathematics Subject Classification. Primary 40D15, 40F05, 40G99.

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...

We define weighted mean summability method of double sequences in intuitionistic fuzzy normed spaces(IFNS), and obtain necessary sufficient Tauberian conditions under which convergence IFNS follows from their summability. This study reveals also results for some known summation methods the special cases.

In this paper, we introduce the notions of [V,λ ]-summability and λ−statistical convergence of function by taking a nonnegative real-valued Lebesque measurable function in the interval (1,∞) and introduce new notions, namely, [V,λ ] (I )− summability, and Iλ−statistical convergence of function. We mainly examine the relation between these two new methods.

In this paper, we introduce the concepts of weighted ideal statistical convergence or SN (I)-convergence and I − (N, pn)-summability. We also establish the relations between our new methods. Further, we determine a Korovkin type approximation theorem through I − (N, pn)-summability. −−−−−−−−−−−−−−−−−−−−−−−−−−−−

In this paper, we establish a new theorem on | A, pn |k summability factors of Fourier series using matrix transformation, which generalizes a main theorem of Bor [6] on ∣∣N̄, pn∣∣k summability factors of Fourier series. Also some new results have been obtained.

Many sequence spaces arise from different concepts of summability. Recent results obtained by Altay, Başar and Malkowsky [2] are related to strong Cesàro summability and boundedness. They determined β−duals of the new sequence spaces and characterized some classes of matrix transformations on them. Here, we will present new results supplementing their research with the characterization of class...

In this study we introduce the concepts of statistical convergence of order β and strong p−Cesàro summability of order β for sequences of fuzzy numbers. Also, we give some relations between the statistical convergence of order β and strong p−Cesàro summability of order β and construct some interesting examples.

the object of this paper is to establish a summability factor theorem for summabilitya, , k  1 k  where a is the lower triangular matrix with non-negative entries satisfying certain conditions.