Journal of Optimization Theory and Applications

, Volume 146, Issue 2, pp 347–357 | Cite as

Auxiliary Principle and Algorithm for Mixed Equilibrium Problems and Bilevel Mixed Equilibrium Problems in Banach Spaces



A new class of bilevel mixed equilibrium problems is introduced and studied in real Banach spaces. By using the auxiliary principle technique, new iterative algorithms for solving the mixed equilibrium problems and bilevel mixed equilibrium problems are suggested and analyzed. Strong convergence of the iterative sequences generated by the algorithms is proved under suitable conditions. The behavior of the solution set of the bilevel mixed equilibrium problem is also discussed.


Mixed equilibrium problems Bilevel mixed equilibrium problems Monotonicity Auxiliary principle Banach spaces 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.College of Mathematics and Software ScienceSichuan Normal UniversityChengduChina

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