Surjectivity results for ϕ-accretive set-valued mappings

David Downing

Vol. 77 (1978), No. 2, 381–388

DOI: 10.2140/pjm.1978.77.381

Abstract

Let X and Y be Banach spaces. A mapping f : X → 2^Y is said to be locally strongly ϕ-accretive if for each y₀ ∈ Y and r > 0 there exists a constant c > 0 such that if z ∈ f(X) ∩ B_r(y₀) and x ∈ f⁻¹(z), then for all u sufficiently near x and w ∈ f(u) : (ϕ(x−u),(w −z)) ≧ c∥x−u∥², where ϕ : X → Y ^∗ is a suitably restricted mapping. A number of surjectivity results are obtained for this class of mappings, along with some other basic results.

Mathematical Subject Classification 2000

Primary: 47H06

Milestones

Received: 29 November 1977

Revised: 3 March 1978

Published: 1 August 1978