Convergence Theorems for Pointwise Asymptotically Strict Pseudo-Contractions in Hilbert Spaces. (3rd March 2016)

• Record Type: Journal Article
• Authors: Balooee, Javad; Cho, Yeol Je; Roohi, Mehdi
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 3(2016)
• Page Start: 284
• Page End: 303
• Publication Date: 2016-03-03
• Subjects: Common fixed point -- Mann's iterative method -- monotone hybrid method -- pointwise asymptotically ϕ-strict pseudo-contraction -- projection operator -- projection technique -- weak and strong convergence; 47H09 -- 47J05 -- 47H25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1144071
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: A new class of contractive mappings called pointwise asymptotically ϕ-strict pseudo-contractions in Hilbert spaces is introduced and weak convergence of the sequence generated by Mann's iterative scheme to a fixed point of a uniformly Lipschitzian and pointwise asymptotically ϕ-strict pseudo-contractive mapping T in a Hilbert space is established. Also, a new kind of monotone hybrid method which is a modification of Mann's iterative scheme for finding a common fixed point of an infinitely countable family of uniformly Lipschitzian and pointwise asymptotically ϕ-strict pseudo-contractive mappings is proposed. Strong convergence of the sequence generated by the proposedmonotone hybrid method for an infinitely countable family of uniformly Lipschitzian and pointwise asymptotically ϕ-strict pseudo-contractive mappings in a Hilbert space is also shown. The results presented in this article extend and improve some known results in the literature.