一般空间中逐次渐近Φ-强伪压缩型算子的具误差的多种迭代间的收敛性和稳定性的等价问题

The Equivalence Problem of the Convergence and Stability between a Variety of Iterations with Errors for Successively Asmptotically Φ-Strongly Pseudocontractive Type Operators in General Spaces

关于多种迭代间收敛性的等价问题已有不少非线性分析学者进行了研究,并对2003年B.E.Rhoades和S.M.Solutz两位教授提出的猜想做出了部分肯定的回答.我们将对一般Banach空间中更具一般意义的算子——逐次渐近Φ-强伪压缩型算子证明了具误差的修正Mann迭代和具误差的修正p步Noor迭代分别强收敛于该算子的不动点是等价的,并给出了相应的T-稳定性间也是等价的,从而从更一般的意义上来肯定地回答Rhoades和Soltuz于2003年所提出的猜想.

The equivalence problem of a variety of iterations of the convergence is a main topic in nonlinear analysis, some nonlinear experts give a partly affirmative answer to the conjecture raised by B.E. Rhoades and S.M. Soltuz in 2003. The purpose of this paper is to prove the equivalence of the convergence between the modified Mann and p - step iterations with errors for successively asmptotically strongly - pseudocontractive type operators in general space, and the respective equivalence of T - stability is also given. So, the more generalized affirmative answer is given to the conjecture in a more general sense.