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Quadratic inequalities for functionals in l∞

Herzog Gerd, Kunstmann Peer Chr.

Opuscula Mathematica

2021

Vol. 41, no. 3

437--446

For a class of operators T on l∞ and T-invariant functionals φ we prove inequalities between φ(x), φ(x2) and the upper density of the sets [formula]. Applications are given to Banach limits and integrals.

Boundary value problems with solutions

Herzog Gerd, Kunstmann Peer Chr.

Opuscula Mathematica

2019

Vol. 39, no. 1

49--60

By means of the continuation method for contractions we prove the existence of solutions of Dirichlet boundary value problems in convex sets. As an application we prove the existence of concave solutions of certain boundary value problems in ordered Banach spaces.