Bilevel Generalized Mixed Equilibrium Problems Involving Generalized Mixed Variational-Like Inequality Problems in Reflexive Banach Spaces

DING Xie-ping

doi:10.3879/j.issn.1000-0887.2011.11.010

Volume 32 Issue 11

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DING Xie-ping. Bilevel Generalized Mixed Equilibrium Problems Involving Generalized Mixed Variational-Like Inequality Problems in Reflexive Banach Spaces[J]. Applied Mathematics and Mechanics, 2011, 32(11): 1361-1377. doi: 10.3879/j.issn.1000-0887.2011.11.010

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Bilevel Generalized Mixed Equilibrium Problems Involving Generalized Mixed Variational-Like Inequality Problems in Reflexive Banach Spaces

doi: 10.3879/j.issn.1000-0887.2011.11.010

DING Xie-ping

College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610068, P. R. China

Received Date: 2011-04-25
Rev Recd Date: 2011-09-03
Publish Date: 2011-11-15

Abstract

Abstract

A new class of bilevel generalized mixed equilibrium problems(BGMEP)involving generalized mixed variational-like inequality problems was introduced and studied in reflexive Banach spaces. First,an auxiliary generalized mixed equilibrium problem(AGMEP)to compute the approximate solutions of the bilevel generalized mixed equilibrium problems involving generalized mixed variational-like inequality problems was introduced.By using a minimax inequality,the existence and uniqueness of solutions of the AGMEP was proved under quite mild conditions without any coercive assumptions.By using auxiliary principle technique,new iterative algorithm to compute the approximate solutions of the BGMEP were suggested and analyzed.The strong convergence of the iterative sequences generated by the algorithms was proved under quite mild conditions without any coercive assumptions.These results are new and generalize some recent results in this field.

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