International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 4, Pages 677-680
doi:10.1155/S0161171298000933
Fixed points of a certain class of mappings in spaces with uniformly normal structure
Jong Soo Jung1
, Balwant Singh Thakur2
and Daya Ram Sahu3
1Department of Mathematics, Dong-A University, Pusan 607-714, Korea
2Govt. B. H. S. S. Gariaband, Dist. Raipur, 493889, M. P., India
3Govt. H. S. S. Kumhari, Dist. Durg, 490042, M. P., India
Abstract
A fixed point theorem is proved in a Banach space E which has uniformly normal structure for asymptotically regular mapping T satisfying: for each x,y in the domain and for n=1,2,⋯,‖Tnx−Tny‖≤an‖x−y‖+bn(‖x−Tnx‖+‖y−Tny‖)+cn(‖x−Tny‖+‖y−Tny‖), where an,bn,cn are nonnegative constants satisfying certain conditions. This result generalizes a fixed point theorem of Górnicki [1].