Fixed points of a certain class of mappings in spaces with uniformly normal structure - Jong Soo Jung; Balwant Singh Thakur; Daya Ram Sahu (International Journal of Mathematics and Mathematical Sciences)
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].