Variational inequalities for ΦΦ-pseudo-contractive mappings

Usually, results on ϕϕ-strongly accretive operators involve various assumptions on the function ϕϕ, such as continuity, being positive, and/or being strictly increasing. However, by redefining this function, we are able to eliminate all these additional assumptions, and leave only the positiveness condition: ϕ(t)>0ϕ(t)>0 for t>0t>0. This fact allows us to extend a theorem of Deimling and obtain a general result for the solvability of a variational inequality for ϕϕ-strongly pseudo-contractive mappings.