Let Sβ := {z ∈ C : | Im z| < β} be a strip in the complex plane. For fixed integer r ≥ 0 let Hr ∞,β denote the class of 2π-periodic functions f , which are analytic in Sβ and satisfy |f(r)(z)| ≤ 1 in Sβ . Denote by Hr,R ∞,β the subset of functions from Hr ∞,β that are real-valued on the real axis. Given a function f ∈ Hr ∞,β , we try to recover f(ζ) at a fixed point ζ ∈ R by an algorithm A on t...

in this paper, for a complete lattice l, we introduce interval-valued l-fuzzy ideal (prime ideal) of a near-ring which is an extended notion of fuzzy ideal (prime ideal) of a near-ring. some characterization and properties are discussed.

‎it is well known that every (real or complex) normed linear space $l$ is isometrically embeddable into $c(x)$ for some compact hausdorff space $x$‎. ‎here $x$ is the closed unit ball of $l^*$ (the set of all continuous scalar-valued linear mappings on $l$) endowed with the weak$^*$ topology‎, ‎which is compact by the banach--alaoglu theorem‎. ‎we prove that the compact hausdorff space $x$ can ...

Predicting class probabilities and other real-valued quantities is often more useful than binary classification, but comparatively little work in PAC-style learning addresses this issue. We show that two rich classes of real-valued functions are learnable in the probabilisticconcept framework of Kearns and Schapire. Let X be a subset of Euclidean space and f be a real-valued function on X. We s...

Let K be a compact Hausdorff space and C(K) the Banach space of all real-valued continuous functions on K , with the sup-norm. Types over C(K) (in the sense of Krivine and Maurey) can be uniquely represented by pairs ( ,u) of bounded real-valued functions on K , where is lower semicontinuous, u is upper semicontinuous, ≤ u, and (x) = u(x) for all isolated points x of K . A condition that charac...

We introduce a domain-theoretic framework for differential calculus. We define the set of primitive maps as well as the derivative of an interval-valued Scott continuous function on the domain of intervals, and show that they are dually related, providing an extension of the classical duality of differentiation and integration as in the fundamental theorem of calculus. It is shown that, for loc...

A sufficient condition for the insertion of a contra-continuous (resp. Baire-one) function between two comparable real-valued functions is given on the topological spaces that Λ-sets are open (resp. Gδ-sets).

It is known that the subdifferential of a lower semicontinuous convex function f over a Banach space X determines this function up to an additive constant in the sense that another function of the same type g whose subdifferential coincides with that of f at every point is equal to f plus a constant, i.e., g = f + c for some real constant c. Recently, Thibault and Zagrodny introduced a large cl...

For a Hausdorff zero-dimensional topological space X and totally ordered field F with interval topology, let $$C_c(X,F)$$ be the ring of all F-valued continuous functions on countable range. It is proved that if either an uncountable or subfield $${\mathbb {R}}$$ , then structure $$\beta _0X$$ Banaschewski Compactification X. The ideals $$\{O^{p,F}_c:p\in \beta _0X\}$$ in are introduced as modi...