We prove that if X is an infinite dimensional Banach lattice with a weak unit then there exists a probability space (Ω,Σ, μ) so that the unit sphere S(L1(Ω,Σ, μ) is uniformly homeomorphic to the unit sphere S(X) if and only if X does not contain l ∞’s uniformly.

We study no-gap second-order optimality conditions for a non-uniformly convex and non-smooth integral functional. The functional is extended to the space of measures. obtained derivatives contain integrals on lower-dimensional manifolds. proofs utilize pre-conjugate, which an continuous functions. Applications optimal control problems are given.

The purpose of this paper is to introduce and consider new hybrid proximal-type algorithms for finding a common element of the set EP of solutions of a generalized equilibrium problem, the set F S of fixed points of a relatively nonexpansive mapping S, and the set T−10 of zeros of a maximal monotone operator T in a uniformly smooth and uniformly convex Banach space. Strong convergence theorems ...

and Applied Analysis 3 by φ(ε) := L[y+εη] and f(t, ε) := L(t, yσ(t)+εησ(t), yΔ(t)+ εη Δ (t)). If ∂f/∂ε is continuous in ε, uniformly in t, then

The metabolism of r-lactate and pyruvate, labeled uniformly with 14C, by epididymal fat pad tissue of fasted and fasted-refed rats was studied. In tissue of fasted-refed rats, pyruvate and L-lactate were utilized at equal rates. L-Lactate was nearly all converted into CO2 and fatty acids, and pyruvate into COZ, fatty acids, and L-lactate. The incorporation of 14C into glycerol was very low. L-L...