On Uniformly Generalized Lipschitzian Mappings
1 Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India
2 Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt
Fixed Point Theory and Applications 2010, 2010:692401 doi:10.1155/2010/692401Published: 17 May 2010
We consider another class of generalized Lipschitzian type mappings and utilize the same to prove fixed point theorems for asymptotically regular and uniformly generalized Lipschitzian one-parameter semigroups of self-mappings defined on bounded metric spaces equipped with uniform normal structure which yield corresponding results in respect of semigroup of iterates of a self-mapping as corollaries. Our results also generalize some relevant results due to the work of Lim and Xu (1995), Yao and Zeng (2007), and Soliman (2009).