Existence and algorithms for the bilevel new generalized mixed equilibrium problems in Banach spaces

Autor:	Rabian Wangkeeree, Panu Yimmuang
Rok vydání:	2012
Předmět:	Mathematics::Functional Analysis Computational Mathematics Pseudo-monotone operator Approximation property Applied Mathematics Eberlein–Šmulian theorem Interpolation space Uniformly convex space Banach manifold Lp space C0-semigroup Algorithm Mathematics
Zdroj:	Applied Mathematics and Computation. 219:3022-3038
ISSN:	0096-3003
DOI:	10.1016/j.amc.2012.09.030
Popis:	In this paper, we introduce and analyze the new generalized mixed equilibrium problems (NGMEP) and the bilevel new generalized mixed equilibrium problems (BNGMEP) in Banach spaces. First, by using a minimax inequality, some new existence theorems of the solution and the behavior of solution set for the NGMEP and the BNGMEP are obtained in both arbitrary Banach spaces with the coercive conditions and a reflexive Banach space without the coercive conditions. Next, by using auxiliary principle technique, some new iterative algorithms for solving the NGMEP and the BNGMEP are suggested and analyzed. The strong convergence of the iterative sequences generated by the algorithms are also proved in both arbitrary Banach spaces with the coercive conditions and a reflexive Banach space without the coercive conditions. These results are new and generalize some recent results in this field.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::d92a6abc14acae6c9e897c0b1300d1be https://doi.org/10.1016/j.amc.2012.09.030 Zobrazit plný text záznamu Full Text from ScienceDirect