Abstract
It is shown that in a Banach space X with weak uniform normal structure, every demicontinuous asymptotically regular nearly Lipschitzian self-mapping T with lim supn→∞η(Tn)<WCS(X) defined on a weakly compact convex subset C of X satisfies the (ω)-fixed point property. We show that if X has a uniformly Gâteaux differentiable norm, then the set of fixed points of every asymptotically pseudocontractive nearly nonexpansive mapping T is nonempty and a sunny nonexpansive retract of C. Further, we study the approximation of fixed points of T by Halpern type iteration process: xn+1=αnu+(1−αn)Tnxnfor alln∈N, where u∈C and {αn} is a sequence in (0,1) satisfying appropriate conditions. Our results improve several known existence and convergence fixed point theorems in general Banach spaces for a wider class of nonlinear mappings which are not necessarily Lipschitzian.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.