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

Volume 9, Issue 5, pp 2959--2970 http://dx.doi.org/10.22436/jnsa.009.05.88

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Authors

Zeqing Liu - Department of Mathematics, Liaoning Normal University Dalian, Liaoning 116029, P. R. China. Pingping Zheng - Department of Mathematics, Liaoning Normal University Dalian, Liaoning 116029, P. R. China. Jeong Sheok Ume - Department of Mathematics, Changwon National University, Changwon 641-773, Korea. Shin Min Kang - Department of Mathematics and the Research Institute of Natural Science, Gyeongsang National University, Jinju 660-701, Korea.

Abstract

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.

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Keywords

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

MSC

•  47J20
•  49J40

References

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