Applied Mathematics and Mechanics (English Edition) ›› 2000, Vol. 21 ›› Issue (11): 1256-1263.

• Articles • Previous Articles     Next Articles

ITERATIVE PROCESS TO φ-HEMICONTRACTIVE OPERATOR AND φ-STRONGLY ACCRETIVE OPERATOR EQUATIONS

DING Xie-ping ZHANG Hong-lin   

  1. Department of Mathematics, Sichuan Normal University, Chengdu 610066, P R China
  • Received:1999-06-21 Revised:2000-09-20 Online:2000-11-18 Published:2000-11-18
  • Supported by:

    the National Natural Science Foundation of China(19871059)

Abstract: Let E be an arbitrary real Banach space and K be a nonempty closed convex subsets of E.Let T:KK be a uniformly continuous Φ hemicontractive operator with bounded range and {an},{bn},{cn},{an},{bn},{cn} be sequences in[0,1] satisfying: 1)an+bn+cn=an+bn+cn=1.∀n=0;ii)limbn=limbn;iii) ;iv)cn-ο(bn). For any given x0,u0,v0K, define the Ishikawa type iterative sequence {xn} as follows:

where {un} and {vn} are bounded sequences in K.Then {xn} converges strongly to the unique fixed point of T.Related result deals with the convergence of Ishikawa type iterative sequence to the solution of Φ-strongly accretive operator equations.

2010 MSC Number: 

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