Some Fixed Point Theorems for Kannan Mappings

2000 Mathematics Subject Classification: Primary: 47H10; Secondary: 54H25.

Some results on the existence and uniqueness of fixed points for Kannan mappings on admissible subsets of bounded metric spaces and on bounded closed convex subsets of complete convex metric spaces having uniform normal structure are proved in this paper. These results extend and generalize some results of Ismat Beg and Akbar Azam [Ind. J. Pure Appl. Math. 18 (1987), 594-596], A. A. Gillespie and B. B. Williams [J. Math. Anal. Appl. 74 (1980), 382-387] and of Yoichi Kijima and Wataru Takahashi [Kodai Math Sem. Rep. 21 (1969), 326-330].