Auxiliary Principle and Approximation Solvability for a System of New Generalized Mixed Equilibrium Problems in Reflexive Banach Spaces

DING Xie-ping

doi:10.3879/j.issn.1000-0887.2011.02.010

Volume 32 Issue 2

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DING Xie-ping. Auxiliary Principle and Approximation Solvability for a System of New Generalized Mixed Equilibrium Problems in Reflexive Banach Spaces[J]. Applied Mathematics and Mechanics, 2011, 32(2): 221-231. doi: 10.3879/j.issn.1000-0887.2011.02.010

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Auxiliary Principle and Approximation Solvability for a System of New Generalized Mixed Equilibrium Problems in Reflexive Banach Spaces

doi: 10.3879/j.issn.1000-0887.2011.02.010

DING Xie-ping

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

Received Date: 2010-09-16
Rev Recd Date: 2010-01-05
Publish Date: 2011-02-15

Abstract

Abstract

A system of new generalized mixed equilibrium problems involving generalized mixed variational-like inequality problems (SGMEP) was introduced and studied in reflexive Banach spaces. First,a system of auxiliary generalized mixed equilibrium problems (SAGMEP) for solving the SGMEP was introduced. The existence and uniqueness of the solutions of the SAGMEP was proved under quite mild assumptions without any coercive conditions in reflexive Banach spaces. Next,by using the auxiliary principle technique,a new iterative algorithm for solving the SGMEP was suggested and analyzed. Finally,the strong convergence of the iterative sequences generated by the algorithm was also proved under quite mild assumptions without any coercive conditions. These results improve,unify and generalize some recent results in this field.
- system of generalized mixed equilibrium problems,
- auxiliary principle,
- iterative algorithm,
- reflexive Banach space

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References(16)

References

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