A simple structure of the multiple Laguerre polynomial expansions is used to study the Cess aro summability above the critical index for the convolution type Laguerre expansions. The multiple Laguerre polynomial expansion of an`1-radial function f 0 (jxj) is shown to be an`1-radial function that coincides with the Laguerre polynomial expansion of f 0 , which allows us to settle the problem of s...

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.

Let $(u_n)$ be a sequence of fuzzy numbers.  We recover the slow oscillation of $(u_n)$ of fuzzy numbers from the Ces`{a}ro summability of its generator sequence and some additional conditions imposed on $(u_n)$. Further, fuzzy analogues of some well known classical Tauberian theorems for Ces`{a}ro summability method are established as particular cases.

*Correspondence: [email protected] 1Faculty of Education, Harran University, Şanlıurfa, Turkey Full list of author information is available at the end of the article Abstract New concepts of fλ,μ-statistical convergence for double sequences of order α̃ and strong fλ,μ-Cesàro summability for double sequences of order α̃ are introduced for sequences of (complex or real) numbers. Furthermore, we giv...