Strong Convergence for Hybrid Implicit S‐Iteration Scheme of Nonexpansive and Strongly Pseudocontractive Mappings

Shin Min Kang, Arif Rafiq, Faisal Ali and Young Chel Kwun

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: Let K be a nonempty closed convex subset of a real Banach space E, let S : K → K be nonexpansive, and let T : K → K be Lipschitz strongly pseudocontractive mappings such that p ∈ F(S)∩F(T) = {x ∈ K : Sx = Tx = x} and ∥x − Sy∥ ≤ ∥Sx − Sy∥ and ∥x − Ty∥ ≤ ∥Tx − Ty∥ for all x, y ∈ K. Let {βn} be a sequence in [0, 1] satisfying (i) ∑n=1∞βn=∞; (ii) limn→∞⁡βn = 0. For arbitrary x0 ∈ K, let {xn} be a sequence iteratively defined by xn = Syn, yn = (1 − βn)xn−1 + βnTxn, n ≥ 1. Then the sequence {xn} converges strongly to a common fixed point p of S and T.

Date: 2014
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2014/735673

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:735673

Access Statistics for this article

More articles in Abstract and Applied Analysis from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().