Fixed point theorems for 1-set weakly contractive and pseudocontractive operators on an unbounded domain

Abstract

We establish new fixed point results for some nonlinear weakly condensing, 1-set weakly contractive, pseudo-contractive and nonexpansive operators defined on unbounded domains under different boundary conditions as well as other additional assumptions. An existence result of positive eigenvalues and eigenvectors for nonlinear weakly condensing operators and an application to generalized Hammerstein integral equations are given.