THE INVARIANCE OF DOMAIN FOR $k$-SET-PSEUDO-CONTRACTIVE OPERATORS IN BANACH SPACES
THE INVARIANCE OF DOMAIN FOR $k$-SET-PSEUDO-CONTRACTIVE OPERATORS IN BANACH SPACES
We introduce a new family of nonlinear operators called $k$-set-pseudo-contractions where several well-known mappings, such as, the condensing mappings (for $k=1$) and the compact perturbations of $k$-pseudo-contractive mappings are embraced in the class of $k$-set-pseudo-contractions. We prove an invariance of domain theorem and (as a consequence) a fixed point theorem …