Xue Zhiqun, Zhou Haiyun. Iterative Approximation with Errors of Fixed Point for a Class of Nonlinear Operation with a Bounder Range[J]. Applied Mathematics and Mechanics, 1999, 20(1): 93-98.
 Citation: Xue Zhiqun, Zhou Haiyun. Iterative Approximation with Errors of Fixed Point for a Class of Nonlinear Operation with a Bounder Range[J]. Applied Mathematics and Mechanics, 1999, 20(1): 93-98.

# Iterative Approximation with Errors of Fixed Point for a Class of Nonlinear Operation with a Bounder Range

• Rev Recd Date: 1998-09-11
• Publish Date: 1999-01-15
• Let X be a uniformly smooth real Banach space. Let T:X→X be a continuous and strongly accretive operator. For a given ∀fX,define S:XxX,for all ∀xX,Let {αn}n=0 be two real sequences in(0,1) satisfying:(ⅰ)αn→0,βn→0(n→∞);.Assume that {un}n=0 and {vn}n=0 are two sequences in X satisfying ‖un‖= o (An) and ‖vn‖→0 as n→∞].For arbitrary x0X, the iteration sequence {xn} is defined by Moreover, suppose that {Snxn} and {Syn} are bounded, then {xn} converges strongly to the unique fixed point of S.
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