Abstract
Abstract We prove strong convergence of the sequence generated by implicit viscosity approximation method involving a multivalued nonexpansive mapping in framework of CAT(0) space. Under certain appropriate conditions on parameters, we show that such a sequence converges strongly to a fixed point of the mapping which solves a variational inequality. We also present some convergence results for the implicit viscosity approximation method in complete ℝ-trees without the endpoint condition.
Highlights
[9] If C is a closed convex subset of a complete CAT(0) space E and T : C → K(C) is a nonexpansive mapping, the conditions {xn} ∆-converges to x and d(xn , Txn) → 0 imply x ∈ F(T)
Let C be a nonempty closed convex subset of a Hilbert space E and T : C → C, the fixed point set of T is denoted by F(T), that is, F(T) = {x ∈ C : x = Tx}
We prove strong convergence of the sequence generated by implicit viscosity approximation method involving a multivalued nonexpansive mapping in framework of CAT(0) space
Summary
[9] If C is a closed convex subset of a complete CAT(0) space E and T : C → K(C) is a nonexpansive mapping, the conditions {xn} ∆-converges to x and d(xn , Txn) → 0 imply x ∈ F(T). The sequence generated by (2) converges strongly to a fixed point x* of the nonexpansive mapping T, which solves the variational inequality
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
