Fixed point theorem and nonlinear complementarity problem in Hilbert spaces

Wang, Hongjun¹ ; Zheng, Yuchun¹

¹ 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

Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 5, p. 1957-1964.

Résumé

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.

Détail

DOI : 10.22436/jnsa.009.05.02

Classification : 47H10, 54H25, 49J40, 47H05, 47H04, 65J15
Keywords: Fixed point, strongly monotone type, complementarity problem, iteration.

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