JournalspmVol. 68 / No. 2DOI 10.4171/pm/1884

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

  • Afif Ben Amar

    Université de Gafsa, Tunisia
  • Jesús Garcia-Falset

    Universitat de València, Burjassot (València), Spain
Fixed point theorems for 1-set weakly contractive and pseudocontractive operators on an unbounded domain cover

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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.