Onweak and strong convergence of an explicit iteration process for a total asymptotically quasi-I-nonexpansive mapping in banach space

Purtas Y.

Filomat, vol.28, no.8, pp.1699-1710, 2014 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 28 Issue: 8
  • Publication Date: 2014
  • Doi Number: 10.2298/fil1408699k
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1699-1710
  • Keywords: Total asymptotically quasi-I-nonexpansive self-mappings, total uniformly L-Lipschitzian maps, explicit iterations, weak and strong convergence, common fixed point, uniformly convex Banach space
  • Manisa Celal Bayar University Affiliated: No

Abstract

In this paper, we introduce a new class of Lipschitzian maps and prove some weak and strong convergence results for explicit iterative process using a more satisfactory definition of self mappings. Our results approximate common fixed point of a total asymptotically quasi-I-nonexpansive mapping T and a total asymptotically quasi-nonexpansive mapping I, defined on a nonempty closed convex subset of a Banach space.