TITLE:
Approximative Method of Fixed Point for Φ-Pseudocontractive Operator and an Application to Equation with Accretive Operator
AUTHORS:
Yixin Wen, Aifang Feng, Yuguang Xu
KEYWORDS:
Duality Mapping; Φ-Pseudo-Contractive Operator; Φ-Accretive Operator; Mann Iterative Sequence with Random Error Terms
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.2 No.1,
January
9,
2014
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.