and Applied Analysis 3 is called a quadratic functional equation. In particular, every solution of the quadratic functional equation is said to be a quadratic mapping. A generalized Hyers-Ulam stability problem for the quadratic functional equation was proved by Skof 7 for mappings f : X → Y , where X is a normed space and Y is a Banach space. Cholewa 8 noticed that the theorem of Skof is still...

Given the irredundant CNF representation φ of a monotone Boolean function f : {0, 1} 7→ {0, 1}, the dualization problem calls for finding the corresponding unique irredundant DNF representation ψ of f . The (generalized) multiplication method works by repeatedly dividing the clauses of φ into (not necessarily disjoint) groups, multiplying-out the clauses in each group, and then reducing the res...

In this paper we introduce and study the notion of plurisubharmonic functions in calibrated geometry. These functions generalize the classical plurisubharmonic functions from complex geometry and enjoy their important properties. Moreover, they exist in abundance whereas the corresponding pluriharmonics are generally quite scarce. A number of the results established in complex analysis via plur...

We establish some fundamental relations between Dirac subbundles L for the generalized Courant algebroid (A⊕A, φ+W ) over a differentiable manifold M and the associated Dirac subbubndles L̃ for the corresponding Courant algebroid Ã⊕ Ã over M × IR.

LetX be a Banach space with dualX∗, and letK be a nonempty subset ofX. A gauge function is a continuous strictly increasing function φ : R → R such that φ 0 0 and limt→∞φ t ∞. The duality mapping Jφ : X → X∗ associated with a gauge function φ is defined by Jφ x : {f ∈ X∗ : 〈x, f〉 ‖x‖‖f‖, ‖f‖ φ ‖x‖ }, x ∈ X, where 〈·, ·〉 denotes the generalized duality pairing. In the particular case φ t t, the ...

and Applied Analysis 3 2. Preliminaries Let E be a real Banach space with dual space E∗. When {xn} is a sequence in E, we denote strong convergence of {xn} to x ∈ E by xn → x and weak convergence by xn ⇀ x, respectively. As usual, we denote the duality pairing of E∗ by 〈x, x∗〉, when x∗ ∈ E∗ and x ∈ E, and the closed unit ball by UE, and denote by R and N the set of all real numbers and the set ...

In this article we prove mixed inequalities for maximal operators associated to Young functions, which are an improvement of a conjecture established in Berra (Proc. Am. Math. Soc. 147(10), 4259–4273, 2019). Concretely, given r ≥ 1, u ∈ A1, \(v^{r}\in A_{\infty }\) and function Φ with certain properties, have that inequality $$ uv^{r}\left( \left\{x\in \mathbb{R}^{n}: \frac{M_{\Phi}(fv)(x)}{ v(...