LetXbe a compact,convex subset of a Banach spaceEandCC(X)be the collection of all non empty compact,coonvex subset ofXequipped with the Hausdorff metrich.Supposeκis a compact,convex subset ofCC(X)and T:(κ,h)(κ,h)is...LetXbe a compact,convex subset of a Banach spaceEandCC(X)be the collection of all non empty compact,coonvex subset ofXequipped with the Hausdorff metrich.Supposeκis a compact,convex subset ofCC(X)and T:(κ,h)(κ,h)is a nonexpansive mapping.Then for anyA 0∈κ,the sequence{A n}defined byA n+1=(A n+TA n)/2converges to a fixed point ofT.The special case thatκconsists of singletons only yields results previously obtained by H.Schaefer,M.Edelstein and S.Ishikawa respectively.展开更多
文摘LetXbe a compact,convex subset of a Banach spaceEandCC(X)be the collection of all non empty compact,coonvex subset ofXequipped with the Hausdorff metrich.Supposeκis a compact,convex subset ofCC(X)and T:(κ,h)(κ,h)is a nonexpansive mapping.Then for anyA 0∈κ,the sequence{A n}defined byA n+1=(A n+TA n)/2converges to a fixed point ofT.The special case thatκconsists of singletons only yields results previously obtained by H.Schaefer,M.Edelstein and S.Ishikawa respectively.
