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 JAMP  Vol.2 No.1 , January 2014
Approximative Method of Fixed Point for Φ-Pseudocontractive Operator and an Application to Equation with Accretive Operator
Abstract: In this paper, Φ-pseudo-contractive operators and Φ-accretive operators, more general than the strongly pseudo-contractive operators and strongly accretive operators, are introduced. By setting up a new inequality, authors proved that if  is a uniformly continuous Φ-pseudo-contractive operator then T has unique fixed point q and the Mann iterative sequence with random errors approximates to q. As an application, the iterative solution of nonlinear equation with Φ-accretive operator is obtained. The results presented in this paper improve and generalize some corresponding results in recent literature.
Cite this paper: Wen, Y. , Feng, A. and Xu, Y. (2014) Approximative Method of Fixed Point for Φ-Pseudocontractive Operator and an Application to Equation with Accretive Operator. Journal of Applied Mathematics and Physics, 2, 21-25. doi: 10.4236/jamp.2014.21004.
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