Proof of Lemma 2. Consider an allocation g(x) that satisfies (IC) and (F). We construct a monotonic g̃(x) that preserves constraints (IC) and (F), but increases the principal’s payoff. We have assumed that F has almost everywhere positive density, so F−1 exists. Define S(t) = ∣∣{y : g(F−1(y)) ≤ t}∣∣, t ∈ R+. Note that S is weakly increasing and satisfies S(t) ∈ [0, 1] for all t. Define g̃(x) = S−...

Abstract Let $F_{\pi }$ be a finite Galois-algebra extension of number field F , with group G . Suppose that }/F$ is weakly ramified and the square root $A_\pi $ inverse different $\mathfrak {D}_{\pi }^{-1}$ defined. (This latter condition holds if, for example, $|G|$ odd.) Erez has conjectured class $(A_\pi )$ in locally free $\operatorname {\mathrm {Cl}}(\mathbf {Z} G)$ $\mathbf G$ equal to C...

For the Fr'{e}chet algebras $(A, (p_k))$ and $(B, (q_k))$ and $n in mathbb{N}$, $ngeq 2$, a linear map $T:A rightarrow B$ is called textit{almost $n$-multiplicative}, with respect to $(p_k)$ and $(q_k)$, if there exists $varepsilongeq 0$ such that$$q_k(Ta_1a_2cdots a_n-Ta_1Ta_2cdots Ta_n)leq varepsilon p_k(a_1) p_k(a_2)cdots p_k(a_n),$$for each $kin mathbb{N}$ and $a_1, a_2, ldots, a_nin A$. Th...

We study the interaction between polynomial space randomness and a fundamental result of analysis, the Lebesgue differentiation theorem. We generalize Ko’s framework for polynomial space computability in R to define weakly pspace-random points, a new variant of polynomial space randomness. We show that the Lebesgue differentiation theorem characterizes weakly pspace random points. That is, a po...

In this paper, the relationships between semicontinuity and preinvexity of fuzzy mappings are investigated. The concepts of intermediate-point preinvex fuzzy mappings and weakly preinvex fuzzy mappings are first introduced, and the authors establish a characterization for a weakly preinvex fuzzy mapping in terms of its epigraph. In this context, a characterization of a preinvex fuzzy mapping in...

Let E be a reflexive Banach space with a uniformly Gâteaux differentiable norm. Suppose that every weakly compact convex subset of E has the fixed point property for nonexpansive mappings. Let C be a nonempty closed convex subset of E, f : C → C a contractive mapping or a weakly contractive mapping , and T : C → C nonexpansive mapping with the fixed point set F T / ∅. Let {xn} be generated by a...

Let E be a reflexive Banach space with a weakly sequentially continuous duality mapping, C be a nonempty closed convex subset of E, f : C → C a contractive mapping (or a weakly contractive mapping), and T : C → C a nonexpansive mapping with the fixed point set F (T ) 6= ∅. Let {xn} be generated by a new composite iterative scheme: yn = λnf(xn)+(1−λn)Txn, xn+1 = (1−βn)yn+βnTyn, (n ≥ 0). It is pr...

In this paper we continue our investigations. begun in the previous paper, of describing the solution sets of constrained extremum problems inf Au). l&l-‘(p) (*) where fand f are twice continuously differentiable functionals on a reflexive Banach space V, and r-‘(p) denotes the level set of the functional f with value p E R. Considering p as a parameter in (*) we obtain results concerning the c...