If a function f is of bounded variation on TN (N ≥ 1) and {φn} is a positive approximate identity, we prove that the area of the graph of f ∗φn converges from below to the relaxed area of the graph of f . Moreover we give asymptotic estimates for the area of the graph of the square partial sums of multiple Fourier series of functions with suitable discontinuities.

Reflectivists consider reflective reasoning crucial for good judgment and action. Anti-reflectivists deny that reflection delivers what reflectivists seek. Alas, the evidence is mixed. So, does confer normative value or not? This paper argues a middle way: can value, but its ability to do this bound by factors such as we might call epistemic identity: an identity involves particular beliefs—for...

We study from an algorithmic viewpoint anonymous games [Mil96, Blo99, Blo05, Kal05]. In these games a large population of players shares the same strategy set and, while players may have different payoff functions, the payoff of each depends on her own choice of strategy and the number of the other players playing each strategy (not the identity of these players). We show that, the intractabili...

We investigate generalized amenability and biflatness properties of various (operator) Segal algebras in both the group algebra, L (G), and the Fourier algebra, A(G), of a locally compact group, G. Barry Johnson introduced the important concept of amenability for Banach algebras in [20], where he proved, among many other things, that a group algebra L1(G) is amenable precisely when the locally ...

We firstly establish an identity for $n$ time differentiable mappings Then, a new inequality for $n$ times differentiable functions is deduced. Finally, some perturbed Ostrowski type inequalities for functions whose $n$th derivatives are of bounded variation are obtained.

Let X,Y, Z be Banach spaces and let u : X×Y → Z be a bounded bilinear map. Given a locally compact abelian group G , and two functions f ∈ L(G,X) and g ∈ L(G,Y ), we define the u -convolution of f and g as the Z -valued function f ∗u g(t) = ∫ G u(f(t− s), g(s))dμG(s) where dμG stands for the Haar measure on G . We define the concepts of vector-valued approximate identity and summability kernel ...

Abstract We prove that for a Banach algebra A having bounded $\mathcal {Z}(A)$ -approximate identity and every $\mathbf {[IN]}$ group G with weight w which is either constant on conjugacy classes or satisfies $w \geq 1$ , {Z}(L^{1}_{w}(G) \otimes ^{\gamma } A) \cong \mathcal {Z}(L^{1}_{w}(G)) . As an application, we discuss the conditions under {Z}(L^{1}_{\omega }(G,A))$ enjoys certain algebrai...