k LIPSCHITZIAN NONEXPANSIVE MAPPINGS IN BANACH SPACES
نویسندگان
چکیده
Let E be a real Banach space with uniformly Gâteaux differentiable norm possessing uniform normal structure. K is a nonempty bounded closed convex subset of E, and { } ( ) ... , 2 , 1 = n Tn is a sequence of − n k Lipschitzian nonexpansive mappings from K into itself such that 1 lim = ∞ → n n k and ( ) 0 1 / ≠ ∞ = n n T F ∩ and f be a contraction on K. Under sutiable conditions on sequence { }, n t we show the sequence { } n x defined as ( ) ( ) n n n n n n n n x T k t x f k t x + − = 1 exists and converges strongly to a fixed point of a mapping T. And we apply it to prove the iterative process defined by K x ∈ 1 and ( ) ( ) n n n n n n n n x T k t x f k t x + − = + 1 1 converges strongly to the same point. HONGLIANG ZUO and MIN YANG 122
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