p-REGULAR MAPPINGS AND ALTERNATIVE RESULTS FOR PERTURBATIONS OF m-ACCRETIVE OPERATORS IN BANACH SPACES

In what follows, the symbol X stands for a real Banach space with norm ‖ · ‖ and (normalized) duality mapping J. Moreover, “continuous” means “strongly continuous” and the symbol “→” (“⇀”) means strong (weak) convergence. The symbol R (R+) stands for the set (−∞,∞) ([0,∞)) and the symbols ∂D, intD, D denote the strong boundary, interior and closure of the set D, respectively. An operator T : X ⊃ D(T )→ Y, with Y another real Banach space, is bounded if it maps bounded subsets of D(T ) onto bounded sets of Y. It is compact if it is continuous and maps bounded subsets of D(T ) onto relatively compact sets of Y. It is called demicontinuous (completely continuous) if it is strong-weak (weakstrong) continuous on D(T ). For a multi-valued operator T : X → 2 and any set A ⊂ X, we set D(T ) = {x ∈ X : Tx 6= ∅} and TA = ⋃ {Tx : x ∈ A} and we always assume that D(T ) 6= ∅. An operator T : X ⊃ D(T ) → 2 is accretive if for every x, y ∈ D(T ) there exists j ∈ J(x− y) such that