The Viscosity Approximation Forward-Backward Splitting Method for Zeros of the Sum of Monotone Operators
Author
Source
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-03-27
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
We investigate the convergence analysis of the following general inexact algorithm for approximating a zero of the sum of a cocoercive operator A and maximal monotone operators B with D(B)⊂H: xn+1=αnf(xn)+γnxn+δn(I+rnB)-1(I-rnA)xn+en, for n=1,2,…, for given x1 in a real Hilbert space H, where (αn), (γn), and (δn) are sequences in (0,1) with αn+γn+δn=1 for all n≥1, (en) denotes the error sequence, and f:H→H is a contraction.
The algorithm is known to converge under the following assumptions on δn and en: (i) (δn) is bounded below away from 0 and above away from 1 and (ii) (en) is summable in norm.
In this paper, we show that these conditions can further be relaxed to, respectively, the following: (i) (δn) is bounded below away from 0 and above away from 3/2 and (ii) (en) is square summable in norm; and we still obtain strong convergence results.
American Psychological Association (APA)
Boikanyo, Oganeditse A.. 2016. The Viscosity Approximation Forward-Backward Splitting Method for Zeros of the Sum of Monotone Operators. Abstract and Applied Analysis،Vol. 2016, no. 2016, pp.1-10.
https://search.emarefa.net/detail/BIM-1094731
Modern Language Association (MLA)
Boikanyo, Oganeditse A.. The Viscosity Approximation Forward-Backward Splitting Method for Zeros of the Sum of Monotone Operators. Abstract and Applied Analysis No. 2016 (2016), pp.1-10.
https://search.emarefa.net/detail/BIM-1094731
American Medical Association (AMA)
Boikanyo, Oganeditse A.. The Viscosity Approximation Forward-Backward Splitting Method for Zeros of the Sum of Monotone Operators. Abstract and Applied Analysis. 2016. Vol. 2016, no. 2016, pp.1-10.
https://search.emarefa.net/detail/BIM-1094731
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1094731