First Order Difference Equations and Proximal Point Algorithm

Consider the following first order evolution equation of monotone type (7.1) { − u ′ ( t ) ∈ A u ( t ) + f ( t ) , u ( 0 ) = u 0 ∈ D ( A ) ¯ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429156908/6b59fc70-f121-4321-b34a-0baf5e3a2176/content/eq1237.tif"/>