Fixed point theorem and nonlinear complementarity problem in Hilbert spaces

Volume 9, Issue 5, pp 1957--1964 http://dx.doi.org/10.22436/jnsa.009.05.02

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Authors

Hongjun Wang - School of Mathematics and Information Science and Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, Henan Normal University, XinXiang 453007, P. R. China. Yuchun Zheng - School of Mathematics and Information Science and Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, Henan Normal University, XinXiang 453007, P. R. China.

Abstract

In this paper, the concept of the strongly monotone type mapping is introduced, which contains the strongly monotone mapping and firmly type nonexpansive mapping as special cases. We show the equivalence between the fixed point problem and the complementarity problem of strongly monotone type mapping. Furthermore, it is obtained that an iteration sequence strongly converges to a unique solution of such a nonlinear complementarity problem on the proper conditions. The error estimation of such an iteration is discussed.

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Keywords

• Fixed point
• strongly monotone type
• complementarity problem
• iteration.

MSC

•  47H10
•  54H25
•  49J40
•  47H05
•  47H04
•  65J15

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