Newton-secant methods with values in a cone

Abstract

We study the variational inclusion 0 ∈ F(x) + G(x) + E(x), (17.1) where X, Y are Banach space D ⊂ X is an open set F : D → Y is a smooth operator, G : D → Y is continuous operator, [., .;G] is a divided difference of order one for G [13] and E : X ⇉ Y is a set-valued operator.