Fixed point results for multivalued contractive maps
1 Department of Mathematics, Faculty of Science For Girls, King Abdulaziz University, P.O. Box 53909, Jeddah 21593, Saudi Arabia
2 Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Fixed Point Theory and Applications 2012, 2012:61 doi:10.1186/1687-1812-2012-61Published: 17 April 2012
Using the concept of u-distance, we prove a fixed point theorem for multivalued contractive maps. We also establish a multivalued version of the Caristi's fixed point theorem and common fixed point result. Consequently, several known fixed point results are either improved or generalized including the corresponding fixed point results of Caristi, Mizoguchi-Takahashi, Kada et al., Suzuki-Takahashi, Suzuki, and Ume.
Mathematics Subject Classification (2000): 47H10; 54H25.