Fixed points of a certain class of mappings in spaces with uniformly normal structure. (1998) - Jung, Jong Soo; Thakur, Balwant Singh; Sahu, Daya Ram
Abstract : A fixed point theorem is proved in a Banach spaceE which has uniformly normal structure for asymptotically regular mappingT satisfying: for eachx, y in the domain and forn = 1, 2, ⋯, ‖ T n x − T n y ‖ ≤ a n ‖ x − y ‖ + b n ( ‖ x − T n x ‖ + ‖ y − T n y ‖ ) + c n ( ‖ x − T n y ‖ + ‖ y − T n y ‖ ), wherea n, b n, c n are nonnegative constants satisfying certain conditions. This result generalizes a fixed point theorem of Górnicki [1].