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.
Share and Cite:
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.
Conflicts of Interest
The authors declare no conflicts of interest.
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