Strong and Δ-Convergence Theorems for Common Fixed Points of a Finite Family of Multivalued Demicontractive Mappings in CAT(0) Spaces. (16th October 2014)

• Record Type: Journal Article
• Authors: Chidume, C. E.; Bello, A. U.; Ndambomve, P.
• Other Names: Reich Simeon Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-10-16
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/805168
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : Let K be a nonempty closed and convex subset of a complete CAT(0) space. LetT i : K → C B K, i = 1, 2, …, m, be a family of multivalued demicontractive mappings such thatF : = ⋂ i = 1 m F ( T i ) ≠ ∅ . A Krasnoselskii-type iterative sequence is shown toΔ -converge to a common fixed point of the familyT i, i = 1, 2, …, m . Strong convergence theorems are also proved under some additional conditions. Our theorems complement and extend several recent important results on approximation of fixed points of certain nonlinear mappings in CAT( 0 ) spaces. Furthermore, our method of the proof is of special interest.