Abstract. In this paper we study the almost everywhere convergence of the expansions related to the self-adjoint extension of the LaplaceBeltrami operator on the unit sphere. The sufficient conditions for summability is obtained. The more general properties and representation by the eigenfunctions of the Laplace-Beltrami operator of the Liouville space L 1 is used. For the orders of Riesz means...

This article provides a power series summability-based Korovkin type approximation theorem for any sequence of fuzzy positive linear operators. Using the notion modulus smoothness, we also derive an associated concerning rate convergence these Furthermore, through example, illustrate that our summability- based Korovin has advantage over proved in seminal paper by Anastassiou (Stud. Univ. Babeş...

Abel, Bord, Cesâro, Holder and Hausdorff, Journal d'Analyse Mathématique vol. 3 (1953-1954) pp. 346-381. 2. -, On a converse of Abel's theorem, Proc. Amer. Math. Soc. vol. 3 (1952) pp. 244-256. 3. W. W. Rogosinski, On Hausdorff methods of summability, Proc. Cambridge Philos. Soc. vol. 38 (1942) pp. 166-192. 4. O. Szász, On the product of two summability methods, Annales de la Société Polonaise ...

3 General results on summability and duality 4 3.1 Total algebras and duality . . . . . . . . . . . . . . . . . . . . . . 4 3.1.1 Series and infinite sums . . . . . . . . . . . . . . . . . . . 4 3.1.2 Summable families in Hom spaces. . . . . . . . . . . . . . 5 3.1.3 Substitutions . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2 Theorem of Cartier-Quillen-Milnor-Moore (analytic form) . ....

0. Preface. This article is a survey of certain aspects of the theory of multiple Fourier and trigonometric series. I t is by no means meant to be a complete survey; for example, it is practically disjoint with the material covered on the subject in Zygmund's book [38, Chapter 17.]. There are eight sections to this survey. §1 is the introduction. §2, §3, and §4 are expository in the sense that ...

A weighted mean matrix, denoted by (N , pn), is a lower triangular matrix with entries pk/Pn, where {pk} is a nonnegative sequence with p0 > 0, and Pn := ∑n k=0 pk. Mishra and Srivastava [1] obtained sufficient conditions on a sequence {pk} and a sequence {λn} for the series ∑ anPnλn/npn to be absolutely summable by the weighted mean matrix (N , pn). Bor [2] extended this result to absolute sum...

In this paper we introduce new Tauberian conditions for Abel summability method that include Hardy Littlewood Tauberian condition [4] as a special case. Mathematics Subject Classification: 40E05

In this paper, using a matrix summability method we obtain a Korovkin type approximation theorem for a sequence of positive linear operators defined on a modular space.

We establish sufficient conditions for summability of integrals with multiplier by $|\overline{W}, p(y)|_k$, $k \geqslant 1$, method.