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Delta-convex mappings between Banach spaces and applications

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L. Veselý L., Zajíček L.

Instytut Matematyczny Polskiej Akademii Nauk

CONTENTS 0. Introduction and notations...................................................5 1. Basic properties of delta-convex mappings.........................8 2. Delta-convex curves..........................................................15 3. Differentiability of delta-convex mappings.........................17 A. First derivative...............................................................17 B. Second derivative of mappings $F: R^n → Y$...............23 4. Superpositions and inverse mappings..............................26 5. Inverse mappings in finite-dimensional case.....................31 6. Examples and applications................................................34 A. Three counterexamples.................................................34 B. Nemyckii and Hammerstein operators............................36 C. Weak solution of a differential equation.........................38 D. Quasidifferentiable functions and mappings..................41 7. Some open problems........................................................44 References...........................................................................47

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1 L. Veselý L.

1 Zajíček L.

1 1989

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Delta-convex mappings between Banach spaces and applications