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Vietnam Journal of Mathematics 40:4(2012) 447-452

Nadler’s Fixed Point Theorem

in Cone Metric Spaces

Do Hong Tan¹ and Nguyen Thi Thanh Ha²

¹Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam

²Department of Mathematics and Informatics, Hanoi National University of

Education, 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam

Received October 31, 2011

Revised December 3, 2011

Abstract. In this note we establish an analogue of Nadler’s fixed point theorem for multivalued contractions in cone metric spaces.

2000 Mathematics Subject Classification. 47H10.

Keywords. Fixed point theorem, multivalued contraction, Hausdorff distance, cone metric space.

Established by Vietnam Academy of Science and Technology & Vietnam Mathematical Society
Published by Springer since January 2013