Sets in the ranges of sums for perturbations of nonlinear 𝑚-accretive operators in Banach spaces

Abstract

Several results are given involving nonlinear range inclusions of the types B + D ⊂ R ( T + C ) ¯ B + D \subset \overline {R(T + C)} and int ⁡ ( B + D ) ⊂ R ( T + C ) \operatorname {int} (B + D) \subset R(T + C) , where B, D are subsets of a real Banach space X, the operator T : X ⊃ D ( T ) → 2 X T:X \supset D(T) \to {2^X} is at least m-accretive, and the perturbation C : X ⊃ D ( C ) → X C:X \supset D(C) \to X is at least compact, or demicontinuous, or m-accretive. Leray-Schauder degree theory is used in most of the results, and extended versions of recent results of Calvert and Gupta, Morales, Reich, and the author are shown to be possible by using mainly homotopies of compact transformations.