Auxiliary principle and iterative algorithms for generalized mixed nonlinear variational-like inequalities

作者：Liu, Zeqing; Zheng, Pingping; Ume, Jeong Sheok^*; Kang, Shin Min

来源：Journal of Nonlinear Sciences and Applications, 2016, 9(5): 2959-2970.

DOI：10.22436/jnsa.009.05.88

• Generalized mixed nonlinear variational-like inequality
• Banach fixed-point theorem
• auxiliary principle technique
• iterative algorithm with errors

The aim of this paper is to study the solvability of a class of generalized mixed nonlinear variational like inequalities in Hilbert spaces. Using the auxiliary principle technique, the Banach fixed-point theorem and an inequality due to Chang and Xiang, we construct two iterative algorithms for finding approximate solutions of the generalized mixed nonlinear variational-like inequality. Under some conditions we prove the existence and uniqueness of solution for the generalized mixed nonlinear variational-like inequality and establish the strong convergence of approximate solutions to the exact solution of the generalized mixed nonlinear variational-like inequality. Our results extend, improve and unify some known results in the literature.

• 出版日期2016
• 单位辽宁师范大学