Affine localization for fixed points of Lipschitz quotient operators

Abstract

We modify and apply new property obtained recently in (Udo-utun, Fixed Point Theory and Applications 2014, 2014:65) and results in (Berinde, Carpath. J. Math. 19(1):7-22, 2003; Nonlinear Anal. Forum 9(1):43- 53, 2004) on (δ, k)−weak contractions to obtain asymptotic fixed point theorems for bi-Lipschitz mappings and Lipschitz quotient mappings in Banach spaces. Our results complement and improve several fixed point theorems for Lipschitzian mappings.