Abstract
The concept of quasi-nonexpansive mappings was initiated in Diaz and Metcalf (Bull. Amer. Math. Soc. 73 (1967), 516–519), further it was generalized by Petryshyn and Williamson (Journal of Mathematical Analysis and Applications 43, no. 2 (1973): 459-497). Further investigating the above work, in this article a Banach space with a relation ρ has been considered, the notion of ρ-preserving and quasi ρ-preserving locally related quasi-nonexpansive mappings has been introduced. It has been shown that every ρ-preserving mapping is a quasi ρ-preserving and every nonexpansive mapping is locally related quasi-nonexpansive but converse may not hold. The necessary and sufficient conditions for the convergence of Picard, Mann and Ishikawa iterations of ρ-preserving, quasi ρ-preserving locally related quasi-nonexpansive mappings are presented.
Original language | English |
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Pages (from-to) | 326-340 |
Number of pages | 15 |
Journal | Numerical Functional Analysis and Optimization |
Volume | 40 |
Issue number | 3 |
DOIs | |
Publication status | Published - Feb 17 2019 |
Keywords
- Ishikawa iterations
- Mann
- Picard
- convergence criteria
- locally related quasi-nonexpansive mappings
- quasi ρ-preserving
ASJC Scopus subject areas
- Analysis
- Signal Processing
- Computer Science Applications
- Control and Optimization