TY - JOUR
T1 - On Convergence of Quasi ρ-preserving Locally Related Quasi-nonexpansive Mappings
AU - Al-Rawashdeh, Ahmed
AU - Mehmood, Nayyar
N1 - Funding Information:
This article is supported by the grant: UPAR(11) 2016, Fund No. 31S249(COS). The second author gratefully acknowledges with thanks the Department of Research Affairs at UAEU. The article has been prepared during the second named author visit as a post doc researcher to the Department of Mathematical Science, UAEU, and would like to thanks the Department of Mathematical Science, UAEU for their support.
Funding Information:
This article is supported by the grant: UPAR(11) 2016, Fund No. 31S249(COS).
Funding Information:
The second author gratefully acknowledges with thanks the Department of Research Affairs at UAEU. The article has been prepared during the second named author visit as a post doc researcher to the Department of Mathematical Science, UAEU, and would like to thanks the Department of Mathematical Science, UAEU for their support.
Publisher Copyright:
© 2018, © 2018 Taylor & Francis Group, LLC.
PY - 2019/2/17
Y1 - 2019/2/17
N2 - 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.
AB - 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.
KW - Ishikawa iterations
KW - Mann
KW - Picard
KW - convergence criteria
KW - locally related quasi-nonexpansive mappings
KW - quasi ρ-preserving
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U2 - 10.1080/01630563.2018.1554585
DO - 10.1080/01630563.2018.1554585
M3 - Article
AN - SCOPUS:85060052427
VL - 40
SP - 326
EP - 340
JO - Numerical Functional Analysis and Optimization
JF - Numerical Functional Analysis and Optimization
SN - 0163-0563
IS - 3
ER -