Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 19, No. 1, pp. 89-100 (2003)

Fixed points and generalized vector equilibra in general topological spaces

Xie Ping Ding and Jong Yeol Park

Sichuan Normal University, Pusan National University

Abstract: In this paper, we first generalize a fixed point theorem due to Tarafdar from topological vector spaces to general topological spaces without linear structure. By using our new fixed point theorem, some new existence theorems of solutions for generalized vector equilibrium problems and generalized implicit vector variational inequality problems are proved under noncompact settings of general topological spaces. Some special cases of our results are also discussed.

Keywords: fixed point, generalized vector equilibria, contractible, topological space

Classification (MSC2000): 91B50

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