The degree of approximation of a function f belonging to Lipschitz class by the Cesàro mean and f ∈ Hα by the Fejér means has been studied by Alexits [4] and Prössdorf [7] respectively. But till now no work seems to have been done to obtain best approximation of functions belonging to generalized Zygmund class, Z (w) r , (r ≥ 1) by product summability means of the form (∆.E1). Z (w) r class is ...

k=1 |ak|, in which C = (cj,k) and the parameter p are assumed fixed (p > 1), and the estimate is to hold for all complex sequences a. The lp operator norm of C is then defined as the p-th root of the smallest value of the constant U : ||C||p,p = U 1 p . Hardy’s inequality thus asserts that the Cesáro matrix operator C, given by cj,k = 1/j, k ≤ j and 0 otherwise, is bounded on lp and has norm ≤ ...

In this article, we generalize results of Lutz, Miyake and Sch afke concerning summability of formal solutions of the Cauchy problem for the complex heat equation. In particular , we show that the type of summability depends on the given initial condition. 0. Introduction. In detail, we will be concerned with the following problem for the complex heat equation (in two complex variables and z): ...

Estimation of gastric acidity has long been regarded as an essential investigation in patients in whom pernicious anaemia is suspected. Gruel, alcohol, insulin, and small doses of histamine which were earlier used to enhance gastric secretion have been replaced by the augmented histamine test meal introduced by Kay (1953). The introduction of methods for direct assay of the content of intrinsic...

k=1 |ak| , in which C = (cj,k) and the parameter p are assumed fixed (p > 1), and the estimate is to hold for all complex sequences a. The lp operator norm of C is then defined as the p-th root of the smallest value of the constant U : ||C||p,p = U 1 p . Hardy’s inequality thus asserts that the Cesáro matrix operator C, given by cj,k = 1/j, k ≤ j and 0 otherwise, is bounded on lp and has norm ≤...

A good amount of work has been done on degree of approximation of functions belonging to Lipα, Lip(α, r), Lip(ξ(t), r) and W (L, ξ(t)) classes using Cesàro and (generalized) Nörlund single summability methods by a number of researchers like Alexits [1], Sahney and Goel [11], Qureshi and Neha [9], Quershi [7, 8], Chandra [2], Khan [4], Leindler [5] and Rhoades [10]. But till now no work seems to...

In the past of two decades, wavelet methods have been adopted enthusiastically in many engineering applications such as signal and image processing. However, like most of the classic orthogonal expansions, wavelet expansions also exhibit Gibbs phenomenon around discontinuities of the original signals. Therefore, the recovered signals using wavelet expansions could be corrupted by the overshoot ...

0 eU(x, p)dp t ∈ C, Re 1 t > α, and we estimate α in terms of ‖v̂0‖μ+2,β and ‖f̂‖μ,β . We show that ‖v̂(·; t)‖μ+2,β < ∞. Existence and t-analyticity results are analogous to Sobolev spaces ones. An important feature of the present approach is that continuation of v beyond t = α−1 becomes a growth rate question of U(·, p) as p → ∞, U being is a known function. For now, our estimate is likely subopt...

Abstract In this article we prove the global existence of weak solutions for a diffuse interface model in bounded domain (both 2D and 3D) involving incompressible magnetic fluids with unmatched densities. The couples Navier–Stokes equations, gradient flow magnetization vector Cahn–Hilliard dynamics describing partial mixing two fluids. density mixture depends on an order parameter modelling (sp...

A blend of matrix summability and Euler transformation methods is used to define Lacunary sequence spaces defined over n-normed space. Then we present the properties this space finally, some inclusion relations are presented.