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BEST PROXIMITY POINT THEOREMS FOR CYCLIC QUASI-CONTRACTION MAPS IN UNIFORMLY CONVEX BANACH SPACES

Part of: Nonlinear operators and their properties Connections with other structures, applications Spaces with richer structures

Published online by Cambridge University Press:  13 October 2016

NGUYEN VAN DUNG  and
VO THI LE HANG
NGUYEN VAN DUNG*
Affiliation:
Nonlinear Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, Viet Nam Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Viet Nam email nguyenvandung2@tdt.edu.vn
VO THI LE HANG
Affiliation:
Faculty of Mathematics and Information Technology Teacher Education, Dong Thap University, 783 Pham Huu Lau Street, Ward 6, Cao Lanh City, Dong Thap Province, Viet Nam email vtlhang@dthu.edu.vn
*
✉ nguyenvandung2@tdt.edu.vn
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Abstract

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In this paper we first give a negative answer to a question of Amini-Harandi [‘Best proximity point theorems for cyclic strongly quasi-contraction mappings’, J. Global Optim.56 (2013), 1667–1674] on a best proximity point theorem for cyclic quasi-contraction maps. Then we prove some new results on best proximity point theorems that show that results of Amini-Harandi for cyclic strongly quasi-contractions are true under weaker assumptions.

Keywords

cyclic quasi-contractionbest proximity pointuniformly convex Banach space

MSC classification

Primary: 47H09: Contraction-type mappings, nonexpansive mappings, $A$-proper mappings, etc.
Secondary: 54E05: Proximity structures and generalizations 54H25: Fixed-point and coincidence theorems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 95 , Issue 1 , February 2017 , pp. 149 - 156
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

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