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

Published online by Cambridge University Press:  13 October 2016

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
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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.

Type
Research Article
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

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