A NEW CLASS OF BILEVEL GENERALIZED MIXED EQUILIBRIUM PROBLEMS IN BANACH SPACES

doi:10.1016/S0252-9602(12)60124-6

摘要/Abstract

摘要：

A new class of bilevel generalized mixed equilibrium problems involving set-valued mappings is introduced and studied in a real Banach space. By using the auxiliary principle technique, new iterative algorithms for solving the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems involving set-valued map-pings are suggested and analyzed. Existence of solutions and strong convergence of the iterative sequences generated by the algorithms are proved under quite mild conditions. The behavior of the solution set of the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems is also discussed. These results are new and gen-eralize some recent results in this field.

关键词: generalized mixed equilibrium problem, bilevel generalized mixed equilib-rium problem involving set-valued mappings, monotonicity, auxiliary prin-ciple, iterative algorithm, Banach space

Abstract:

Key words: generalized mixed equilibrium problem, bilevel generalized mixed equilib-rium problem involving set-valued mappings, monotonicity, auxiliary prin-ciple, iterative algorithm, Banach space

中图分类号:

47J22

丁协平. A NEW CLASS OF BILEVEL GENERALIZED MIXED EQUILIBRIUM PROBLEMS IN BANACH SPACES[J]. 数学物理学报(英文版), 2012, 32(4): 1571-1583.

DING Xie-Ping. A NEW CLASS OF BILEVEL GENERALIZED MIXED EQUILIBRIUM PROBLEMS IN BANACH SPACES[J]. Acta mathematica scientia,Series B, 2012, 32(4): 1571-1583.

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