Generalized solutions of Volterra integral equations of the first kind.
Generalized Solutions to Cauchy Problems.
Generalized Solutions to Semilinear Hyperbolic Systems.
Generalized spectral perturbation and the boundary spectrum
By considering arbitrary mappings from a Banach algebra into the set of all nonempty, compact subsets of the complex plane such that for all , the set lies between the boundary and connected hull of the exponential spectrum of , we create a general framework in which to generalize a number of results involving spectra such as the exponential and singular spectra. In particular, we discover a number of new properties of the boundary spectrum.
Generalized stability of -ternary quadratic mappings.
Generalized strongly -summable sequences defined by Orlicz functions
Generalized Stummel Class and Morrey Spaces
Generalized Taylor expansions of singular functions
Generalized transforms and convolutions.
Generalized Ulam-Hyers stability of Jensen functional equation in Šerstnev PN spaces.
Generalized vector equilibrium-like problems without pseudomonotonicity in Banach spaces.
Generalized vector-valued sequence spaces defined by modulus functions.
Generalized weak peripheral multiplicativity in algebras of Lipschitz functions
Let (X, d X) and (Y,d Y) be pointed compact metric spaces with distinguished base points e X and e Y. The Banach algebra of all -valued Lipschitz functions on X - where is either‒or ℝ - that map the base point e X to 0 is denoted by Lip0(X). The peripheral range of a function f ∈ Lip0(X) is the set Ranµ(f) = f(x): |f(x)| = ‖f‖∞ of range values of maximum modulus. We prove that if T 1, T 2: Lip0(X) → Lip0(Y) and S 1, S 2: Lip0(X) → Lip0(X) are surjective mappings such that for all f, g ∈ Lip0(X),...
Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials: a survey.
Generalized weights for operator Lie algebras
Generalized Weyl-von Neumann Theorems (II).
Generalized-lush spaces and the Mazur-Ulam property
We introduce a new class of Banach spaces, called generalized-lush spaces (GL-spaces for short), which contains almost-CL-spaces, separable lush spaces (in particular, separable C-rich subspaces of C(K)), and even the two-dimensional space with hexagonal norm. We find that the space C(K,E) of vector-valued continuous functions is a GL-space whenever E is, and show that the set of GL-spaces is stable under c₀-, l₁- and -sums. As an application, we prove that the Mazur-Ulam property holds for a larger...
Generalizing normality for operators on Banach spaces: Hyponormality. I.
Generalizing the Johnson-Lindenstrauss lemma to k-dimensional affine subspaces
Let ε > 0 and 1 ≤ k ≤ n and let be affine subspaces of ℝⁿ, each of dimension at most k. Let if ε < 1, and m = O(k + log p/log(1 + ε)) if ε ≥ 1. We prove that there is a linear map such that for all 1 ≤ l ≤ p and we have ||x-y||₂ ≤ ||H(x)-H(y)||₂ ≤ (1+ε)||x-y||₂, i.e. the distance distortion is at most 1 + ε. The estimate on m is tight in terms of k and p whenever ε < 1, and is tight on ε,k,p whenever ε ≥ 1. We extend these results to embeddings into general normed spaces Y.
Generalizzazione di una proposizione di analisi funtoriale. Un'applicazione