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
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
Received 12 September 1996; Revised 4 May 1997
Copyright © 1998 Jong Soo Jung et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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].