Fixed points of a certain class of mappings in spaces with uniformly normal structure

摘要

A fixed point theorem is proved in a Banach spaceEwhich has uniformly normalstructure for asymptotically regular mappingTsatisfying:for eachx,yin the domain and forn=1,2,⋯,‖Tnx−Tny‖≤an‖x−y‖+bn(‖x−Tnx‖+‖y−Tny‖)+cn(‖x−Tny‖+‖y−Tny‖),wherean,bn,cnare nonnegative constants satisfying certain conditions. This result generalizes a fixedpoint theorem of Górnicki [1].