Let (E,F) be a locally convex space. We denote the bounded elements of E by Eb : ={x ∈ E : ‖x‖F = sup ∈F (x)<∞}. In this paper, we prove that if BEb is relatively compact with respect to the F topology and f : I × Eb → Eb is a measurable family of F-continuous maps then for each x0 ∈ Eb there exists a norm-differentiable, (i.e. differentiable with respect to the ‖ · ‖F norm) local solution to t...

We make a spectral analysis of discrete Schrödinger operators on the half-line, subject to complex Robin-type boundary couplings and complex-valued potentials. First, optimal enclosures are obtained for summable Second, general smallness conditions potentials guaranteeing stability established. Third, identity which allows generate Hardy inequalities Dirichlet Laplacian half-line is proved.

In this paper, we use an identity of Fink and present some interesting identities inequalities for real valued functions r-convex respectively. We also obtain generalizations Hardy-Littlewood-P?lya type inequalities. addition, the Cebysev functional Gr?ss find bounds remainder in obtained identities. Finally, result related to Ostrowski