Applications of an HIDS Theorem to the Existence of Fixed Point, Abstract Equilibria and Optimization Problems | Zendy

Wei–Shih Du | Zendy

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Applications of an HIDS Theorem to the Existence of Fixed Point, Abstract Equilibria and Optimization Problems

Author(s) -

Wei–Shih Du

Publication year - 2011

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2011/247236

Subject(s) - mathematics , fixed point theorem , variational principle , equivalence (formal languages) , existence theorem , parametric statistics , brouwer fixed point theorem , fixed point , minification , mathematical analysis , pure mathematics , mathematical optimization , statistics

By applying hybrid inclusion and disclusion systems (HIDS), we establish several vectorial variantsof system of Ekeland's variational principle on topological vector spaces, some existence theorems of system of parametric vectorial quasi-equilibriumproblem, and an existence theorem of system of the Stampacchia-type vectorial equilibrium problem. As an application, a vectorial minimization theorem isalso given. Moreover, we discuss some equivalence relations between our vectorial variant of Ekeland's variational principle, common fixed pointtheorem, and maximal element theorem

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